To pretend is disingenuous though, so it doesn't really work. And people shouldn't have to do it unnecessarily. It's actually sexist in that it discourages the next player if that person's not of the above-mentioned gender. And I'm aware it's not an English test; a fact I prove every time I use "their" and "they" incorrectly.
The problem with assuming the next person's gender in this game is you can't without it appearing that you're playing the game exclusively with a certain other member. This discourages others and is unfair to them. That's why one has no choice but either use the form, i.e., "TPBM puts his/her pants on backward" or "TPBM puts their pants on backward". The first is tediously proper, the second is improper but more fun. Just my humble opinion.