I grew up playing video games. I have played, and still play, a lot of games involving shooting things, punching and kicking things, and colorful explosions. I got hooked on the medium with Williams' "Defender".
I don't play FPSs because they are, with very few exceptions, coded as Games For Guys. I've had a great time playing Portal, System Shock 2, Antichamber, and a few other first person puzzle shoot things, because they are either genderless, or are strongly feminine. (You would destroy me in a high-speed deathmatch because my 'put cursor on dude' skills are minimal - largely because almost every single 'put cursor on dude' game requires me to inhabit the grey/brown shoes of Mancho McGruntsalot, so I really don't feel like playing them.)
I avoid most AAA games for similar reasons. They are all clubhouses with a "NO GURLS ALLOUED" sign hung out front. I played the hell out of Skyrim and Saint's Row 3/4 in no small part because I could make female avatars and the game would happily let me be that. (For that matter, I basically quit buying the 3D GTA games when they stopped having any 'play as another model' codes that I could input to force the game to acknowledge my gender. Even if it did sometimes result in a cutscene where a lady model stood with her legs wide open, talking in a male voice, and dangling a gun in front of her crotch obscenely.)
I have a bunch of lady friends who have spent tons of time playing MMORPGs. I haven't, myself, because I know I'd fall into that hole and never come out - but again: easy access to female avatars right there in the stock game, no hassle, hey maybe we'll welcome women.