The way I look at it, there's always been people who don't fit neatly into male or female definitions, and might not like to called him or her. I think adopting "they" as an agreed solution for those folks is reasonable - we do actually use "they" in the singular quite a lot when we don't mean to imply a particular gender: "If someone wants to get to Camden, they should take the 168 bus." That's technically, grammatically incorrect, but so widely done that I'd say it's a common usage.
So, if folks who would like to see that option in games want to argue for it, that seems fine, to me. But I think it's this proliferation of personal pronouns that gets into silly territory. It's just not feasible to accommodate every way a person might want to be addressed. A while back I read a guidance sheet that was put out on the subject, and it talked about many of the alternative pronouns out there, and it also mentioned that a person must never be referred to as "it", because that's a slur. Then just the other day I saw a debate where everyone declared their pronouns at the start, and one of them was to be addressed as "it".
Surely it's obvious that this just becomes silly, and starts to defeat the point of using pronouns rather than proper nouns in the first place.