Why did Barry Lyndon intentionally shoot to the ground?

As explained here:

Culturally, taking turns displays an even more amplified absurdity of high society than we’ve had so far. Stand still while someone shoots at you. It’s likely that the coin flip itself could seal your fate. And here is the theme of the film. A lot of chance occurrences led Barry to becoming a gentleman and to this duel and the duel itself represents both fate and the absurdity of civilized society. You can make shooting at each other appear gentlemanly, but violence is violence.

Of course, the scene goes deeper than that:

Each of the three moments of gunfire represents a turn in the scene. Bullingdon’s first shot, a misfire, represents an act of fate. He might very well be killed because of a simple mistake. It is interesting that, while building tension, there is a surprise moment.

This surprise allows for this pivotal moment:

However, despite all of the coincidental events and choices that that led Barry down a variety of unknown paths and to this very situation, he seems to have finally received a concrete choice to which he knows the outcome: kill Lord Bullingdon and rid himself of an annoying adversary or spare his life and attempt to heal their relationship and his reputation. Barry chooses the latter and fires his pistol into the ground. Perhaps, Barry was now fully assuming the role of an honorable gentleman.

This duel also fits with the other duels in the movie:

JB: Barry Lyndon is punctuated by no less than three duels: the one that opens the film, in which Barry’s father is killed; the one that sends Barry on the lam, in which Barry appears to kill Captain Quin; and the one near the end of the film, in which Barry and Lord Bullingdon seem determined not to kill one another. Each scene has a slightly different mood—from swift and deadly to drawn out and inconsequential (relatively speaking)—but each scene highlights the absurdities of dueling, and thus the foolishness of any people who would partake in the ritual.

[...]

EH: The duels are indeed one of the primary vehicles for Kubrick’s satire of the “noble” class and their silly, artificial rules for living. As you say, the film opens with a duel, which immediately establishes the absurdity of staking one’s life over minor slights of “honor,” so that a life is erased in mere seconds. This absurdity calls into question the whole concept of honor as it’s understood by the society depicted in this film — duels as presented by Kubrick are not so much showcases for honor and nobility but evidence of fragile egos forced by convention to respond to even the slightest of imagined insults.

The article also puts the final duel into a larger context:

JB: By the time Barry enters into that final duel, he’s seemingly lost everything. We’ve seen him shunned from his old social circle. We’ve watched his son die. And then, in the duel with his stepson, Barry is shot by Lord Bullingdon even after he spares his stepson by intentionally firing into the ground. Barry’s sacrificed shot seems less a matter of etiquette (you wasted a shot, so I will) and more like an olive branch, an admission of guilt, an act of atonement. Barry knows that he has treated his stepson poorly, so he understands Lord Bullingdon’s rage, much like Captain Quin must have understood Barry’s rage all those years ago. There’s a sense when Barry fires his shot into the ground that he hopes Lord Bullingdon will shoot him dead and end his misery, but when Lord Bullingdon announces that he has not received “satisfaction” there’s a subtle expression of surprise that flashes across Barry’s face, as if the last thing he imagined is that Lord Bullingdon would continue with the duel after Barry spared him.

Of course, Barry’s ultimate fate in the duel is the worst thing he can imagine. He isn’t spared. He isn’t killed. He’s maimed, blasted in the leg. In the next scene, the doctor examines Barry’s leg and says he’ll have to amputate. “Lose the leg? What for?” Barry asks. “The simple answer to that is ’to save your life,’” the doctor replies. This, it turns out, is the low point for Barry. Suddenly it registers for him that there’s no coming back from this duel, the way he’d reinvented himself all those years ago. He’ll forever be crippled, and he’ll forever have a physical reminder of his sins. And as Barry comes to this realization, weeping in bed, a church bell tolls in the background.

Possibly Barry Lyndon, for all his flaws, is not capable of cold blooded or hot blooded murder and would rather take his chances of being killed than kill even his enemy.

I note that BCdotWEb's answer quotes this from an unspecified source:

Culturally, taking turns displays an even more amplified absurdity of high society than we’ve had so far. Stand still while someone shoots at you. It’s likely that the coin flip itself could seal your fate.

But it seems to me that standing still while someone shoots at you might not be good for your health, but is an act of self control that has often been chosen voluntarily, and has often been legally enforced on people.

Barry runs away from Ireland and enlists in the British Army, fighting in the Seven Years War (called the French and Indian War in the USA) and later fights in the Prussian Army in the same war.

As an enlisted man, Barry was required to shoot when ordered to shoot, and to not shoot when not ordered to shoot. Among other things, that meant that he could have been severely punished for shooting in battle if not ordered to do so.

For over two hundred years European armies fought in close ranks, the men of each battalion marching together into position and standing up and shooting at the enemy all together, in volleys. Volley fire had a much more demoralizing effect on the enemy that shooting at will did.

In those days the muskets had to be reloaded after every shot, which took time. After firing a volley, a unit was incapable of harming the enemy until they reloaded. As two units marched closer and closer and closer together the men in each unit knew that the probability that the other side would shoot at them was getting higher every second. Every second the tension and the temptation to shoot got stronger and stronger.

Muskets were not very accurate. Many armies didn't use the command to aim when shooting. Instead the command was to level the muskets. Since the two tightly packed units would be facing each other, there wasn't much need to aim the muskets right or left in the horizontal direction. It was hoped that if the muskets were level they wouldn't overshoot or undershoot the enemy.

And the closer to the enemy when the volley was fired, the greater the proportion of musket balls that would hit enemy soldiers and contribute toward winning the battle. If a unit fired too soon to do serious damage to the enemy, the enemy might blast them with a more damaging volley before they could reload and fire again.

Thus many battles in that era began as giant deadly games of chicken, the officers on each side hoping the other side would fire first while still too far away to do serious damage. There were battles where an officer of one side politely ivited for the other side to shoot first and an officer of the other side politely declined.

Thus privates like Barry Lyndon were often ordered to stand and do nothing while the enemy shot at them, until the officers ordered them to shoot back. A soldier who shot back in battle without being ordered to could be punished for disobeying orders.

And in those days officers rarely used guns and rarely shot at the enemy. Instead they led, commanded, directed, and encouraged their men. Barry would have often seen his officers leading under fire without shooting at the enemy. He knew that was expected of an officer and a gentleman, and Barry spent most of his life trying to become accepted as a gentleman.

The non commissioned officers also usually led instead of shooting. And Barry may have known privates who hoped to become non commissioned officers.

And then there were the musicians, the drummers and fifers, whose job was to sound various signals in battle, and to beat the time as the men marched to help them stay in step. Their job description had no place for shooting at the enemy while they were being shot at.

You may note that at that time officers often began their careers as teenagers, and sometimes younger. And you may have heard of drummer boys, teenage and younger boys who served as military drummers. It is certainly possible that a real private in Barry Lyndon's units at that time could have seen boy officers and drummer boys younger than himself, who did their jobs in battle under fire without either running away in fear or shooting at the enemy.

Thus in the era of Barry Lyndon there were at any one time hundreds of thousands of men, and possibly thousands of children, whose jobs required them at times to be shot at without either running away or shooting back.

How did soldiers in that era deal with feelings of guilt for taking part in such bloody slaughters? No doubt to many it was no big deal to kill enemies of their country in battles sanctioned by their government. But many others no doubt felt a lot of guilt for taking part in mass slaughters

The privates - and Barry Lyndon was a private for a few years - could explain away their part, since they almost never aimed at individual enemies and the smoke from a volley would make it impossible for them to see if they hit anyone. Furthermore, the privates were drilled to perform like automations on the battlefield without any initiative, and could claim that they had no choice but to obey like robots orders to fire. If a private shot without orders, and/or aimed at a specific individual person, he would not be able to make that excuse to justify his actions.

The officers, who were mostly gentlemen - the social class that Barry Lyndon spent much of his lifetime becoming a part of - could deny their guilt for the carnage of battle by claiming that they didn't (or very rarely) personally killed anyone (and if so, almost never with a lower class weapon like a musket). They could claim that instead of killing people they directed and ordered the actions of the privates, who were the ones who fired the guns and actually killed the enemies.

The role of a gentleman officer in battle was basically to risk his life in constant danger directing and inspiring his subordinates, without personally killing enemies.

And over time the gentleman's code for duels came to frown more and more on trying to kill the opponent, and more and more to favor showing the duelist's bravery, his willingness to face possible death for his honor.

Over time, gentlemen became more and more convinced that killing people to avenge insults was not ethically justified and was murder, just as the law said. But they were too afraid of being considered cowards by declining challenges to duels. So it became more and more common for gentlemen to decline to shoot, or to shoot into the air or the ground, during duels, showing that they were brave enough to face death in duels, but not savage enough to kill someone in duels.

Thus over time the probability of being killed or seriously injured in a duel got lower and lower.

That was not as good a situation as dueling being abandoned totally by all gentlemen, but it was an great improvement over the time when both parties in a duel would probably intend to kill the opponent.

So from an ethical point of view I do not see the sense of criticizing someone for not shooting at his opponent in a duel or asking why he doesn't shoot at his opponent. That is asking why someone is not evil enough to attempt murder of, in this case, a relative by marriage. And even the most evil persons in history did have some ethical standards; even men who slaughtered millions of innocent victims drew the line somewhere and would not have killed some persons under some circumstances.