A character's ethnic background doesn't need a reason. A character can be of Chinese and Irish descent without it being crucial the story. If you draw a character of some ethnic heritage, that heritage is at least partially clear by the way they're rendered. Ethnicity is an aesthetic; no further explanation is needed. But in video games, being gay is fairly meaingless. What would it mean for Mario to be gay? Nothing, really. His relationship with Peach is almost entirely asexual to begin with, so for Mario to be gay doesn't change the narrative at all. But there's also no opportunity to introduce Mario's gayness into the storyline as it would never be relevant since his love life is never explored. You could have a gay Mortal Kombat character too. We'll retcon Reptile to be gay. And again, it neither adds nor detracts from the game.

Or how about this: Sonic is gay! That actually adds to the narrative. That's why Sonic's not interested in Amy, and why his best friend is a prepubescent boy. No wonder Sega and Michael Jackson got a long so well...

Bottom line is this: if there's room in a narrative for a game to explore a character's love life, there's room for that character to be gay. If the narrative never gets that personal, then there's not.