Yes, I don’t think anyone disagrees with you here. IMO, the rule of thumb is, “Would it be equally funny if the genders were swapped?”, and IMO, the answer is “yes” in this case, because the joke doesn’t rely on sexism.

This is a good rule of thumb, and I think where the joke actually lies. See, it relies on the viewer's familiarity with the Patrick Bateman image, where it's suddenly recontextualised as an image of a man having sex with a corpse. That works because the popular image only focusses on the man and the woman is so depersonalised that there is nothing to indicate whether she's even alive.

The question about whether it would work with the genders swapped depends on whether an equally popular image-of-a-woman-sexually-dominating-a-man-who-is-so-devoid-of-personhood-that-he-could-be-dead exists, and the answer is no, of course not. The man sexually dominating a woman who lacks agency is pervasive throughout our culture because our culture is deeply patriarchal. That's why this image is so common.

That cultural backdrop is the point here. That's why this joke can so easily be misongynistic without triggering people's disgust, because it's not so different from the baseline level of misogyny that we experience every day. If you had to explain this to someone without that background, you would sound like a monster if you were trying to sell it as funny.

As for the origins of the game, there's debate as to where it comes from, mostly from fictional accounts or from stories of mock executions. But yes, the popular imagination comes from Deer Hunter, where you do in fact point it at your own head. There's nothing to indicate the woman agreed to play, however, since her consent isn't part of the equation once she's dead. That was my actual point when I brought up the fact that there's no rulebook for the game.