Were gladiators forced to fight in historical reenactments, as they did in "Gladiator"?

Yes. It is even believed that the Coliseum in Rome was filled with water at times to re-enact sea battles. From the Wiki:

The Colosseum could hold, it is estimated, between 50,000 and 80,000 spectators, having an average audience of some 65,000; it was used for gladiatorial contests and public spectacles such as mock sea battles, animal hunts, executions, re-enactments of famous battles, and dramas based on Classical mythology. The building ceased to be used for entertainment in the early medieval era. It was later reused for such purposes as housing, workshops, quarters for a religious order, a fortress, a quarry, and a Christian shrine.

While the events of the movie were not entirely factual, the concept and presentation was accurate as to what happened there.

Yes, it did happen.

Roman Emperor Lucius Aurelius Commodus, who was infamous during his rule, considered him as a reincarnation of Hercules and used to fight in arena as a gladiator.

From Ancient Origins,

The activities which held Commodus’ attention and with which he spent his time were in the nature of “gladiatorial combat.” He would take to the arena and engage in combat which the Romans viewed as being scandalous and disgraceful. He was very vain, and strongly believed himself to be the reincarnation of Hercules – so much so that he ordered statues of himself be dressed like Hercules, and he ordered that people call him Hercules, son of Zeus.

This article suggests that Romans did reenactment in more spectacular way.

Sometimes, indeed, remarkable liberties were taken with the biographies of the heroes which were “revised” to make them more spectacular and to provide a bloody end. In one of these dramas, of which unfortunately, we do not possess the complete scenario, Daedalus does not reach his destination; as he flies over the arena, his wings fail him. A bear awaits him on the ground.

More examples can be found in this article. For instance,

On the summit was chained a man, half-naked, playing the “poetic” role of the celebrated brigand Selurus, the terror of Sicily, perhaps also of Prometheus chained to his rock. But he was a man of flesh and blood, and one could see from the rise and fall of his chest that he was afraid to die. Before the crowd had finished feasting its eyes on the spectacle, the mountain had fallen to pieces and the “bandit” had been precipitated still alive among the cages of wild beasts, which had been fastened in such a way as to open at the slightest touch.

These other two answers are great, but I would just like to add some more interesting information. Most of this information comes from a great source titled "Murderous Games" on the website www.historytoday.com.

It took many years for historical reenactments to become commonplace.

The Colosseum was dedicated in AD 80 with 100 straight days of "games". In one single day over 3,000 men fought; along with another 9,000 animals being killed.

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The Emperor Trajan, to celebrate his conquest of Dacia (roughly modern Roumania), gave games in AD 108-9 lasting 123 days in which 9,138 gladiators fought and eleven thousand animals were slain. The Emperor Claudius in AD 52 presided in full military regalia over a battle on a lake near Rome between two naval squadrons, manned for the occasion by 19,000 forced combatants. The palace guard, stationed behind stout barricades, which also prevented the combatants from escaping, bombarded the ships with missiles from catapaults. After a faltering start, because the men refused to fight, the battle according to Tacitus 'was fought with the spirit of free men, although between criminals. After much bloodshed, those who survived were spared extermination'.

Mass executions were very popular as can be seen from this excerpt from Seneca, a Roman senator and philosopher.

[He] tells of a visit he once paid to the arena. He arrived in the middle of the day, during the mass execution of criminals, staged as an entertainment in the interval between the wild-beast show in the morning and the gladiatorial show of the afternoon:

All the previous fighting had been merciful by comparison. Now finesse is set aside, and we have pure unadulterated murder. The combatants have no protective covering; their entire bodies are exposed to the blows. No blow falls in vain. This is what lots of people prefer to the regular contests, and even to those which are put on by popular request. And it is obvious why. There is no helmet, no shield to repel the blade. Why have armour? Why bother with skill? All that just delays death.

In the morning, men are thrown to lions and bears. At mid-day they are thrown to the spectators themselves. No sooner has a man killed, than they shout for him to kill another, or to be killed. The final victor is kept for some other slaughter. In the end, every fighter dies. And all this goes on while the arena is half empty.

Here is another interesting fact about The Colosseum. It could seat some 50,000 people. And it had the worlds first retractable roof. Somewhat like modern day stadiums, the Colosseum used a very intricate system of awnings which they called a "Velarium". This system of curtains protected the crowd from the elements such as the sun and rain. But the main use of the velarium was actually to create a ventilation updraft, and circulate the arena with a cool breeze.