What does "And that’s the gambit!" mean?

It's just a mistake by the screenwriter (Michael Waldron) who doesn't understand what a gambit is.

The word that should have been used is dilemma which is a choice between two bad alternatives.

Of the definitions you gave, the third one does seem to work best to describe the gambit, although the other definitions can also work:

3. A remark made to open or redirect a conversation.

In this case, having encountered the two Lokis who were initially dead-set on killing him, his claimed gambit is the remark to redirect the conversation towards the lesser of two evils, as claimed by him. To an extent, one of the Lokis he attempts this gambit on is, in fact, redirected in how they would have taken the conversation as a result.

It could also be the second definition - he is attempting to maneuver himself into a position that both Lokis come to a conclusion that he can't be killed because he is the lesser of two evils. That he didn't entirely succeed to gain a total advantage is beside the point - it was what he had attempted to do.

In other words - his gambit is that by providing them with the information as to what the "tradeoff", "sacrifice", or "decision" that can be made, that this information will allow him to survive the breach of the threshold alive and well. Up until that moment, the Lokis in question did not have the information he just gave them, and his move in response to that is to give them the information, partially as a gamble, but partially as a gloating bluff.

In the context of the first definition regarding chess moves, it would be more of a metaphor - he knows his Queen would likely be sacrificed, so he moves it into a position where he can claim that anyone who takes his Queen ends up facing an easier position to be Checkmated from, in a gambit to ensure an easier win.

He may also be referring to the circular sequence of events regardless of either choice for himself or his variants to "Win" regardless of the choice made here:

From another way to look at it, based on his claim that regardless of whether or not he is killed there, he will end up back in that same position as the head of the TVA later on (Whether as he is now, or his variant that wins the claimed Multiversal War as a result of him dying here now). He could be referring to that situation as a Xanatos Gambit (Warning: TV Tropes link) - that is, regardless of what action is taken at that moment, he will still win, from his point of view.

Or to quote the page linked:

A Xanatos Gambit is a plan for which all foreseeable outcomes benefit the creator — including ones that superficially appear to be failure. The creator predicts potential attempts to thwart the plan, and arranges the situation such that the creator will ultimately benefit even if their adversary "succeeds" in "stopping" them. When faced with a Xanatos Gambit the options are either to accept that the creator will get the upper hand and choose the outcome that is least beneficial to them, or to defeat them by finding a course that they didn't predict.

...

At its most basic, the Xanatos Gambit assumes two possible outcomes for the one manipulated — success or failure. The plan is designed in such a way that either outcome will ultimately further the plotter's goals. A more complex view is offered by the study of probability in which such a gambit is known as a Dutch Book and involves securing bets such that regardless of the outcome the bookie will always pay out less than was bet.

In this case, He Who Remains is confident that killing him is not a sufficient enough course that would not allow him to benefit.

It isn't used traditionally but it can be understood quite easily. When "He Who Remains" says, "And that's the gambit," it is meant to mean the decision. The decision is like a gamble that could be made as a tough decision. You need to choose the right choice but they both are 50/50 in power of result. Simply put, "He Who Remains" is implying that the gambit/decision is either kill him and allow his variant self and other variant forms to come with a conquering war, or take his job as the overseer of time giving "He Who Remains" a retirement. It is a hard choice I know. "And that's the gambit."