The phrase 'gamer girl' gives me an angry twitch now e_e It makes no sense. Like saying, 'male hairdresser' or 'female soldier.'
(As in saying 'I'm a girl gamer' rather than just, 'I'm a gamer' I don't mean to differentiate between the sexes.)
Anyway, I think maybe some guys are looking for a "typical" girl, who will go shopping every Saturday and leave him with his xbox or wear full make-up all the time or cook and clean for them. Maybe they just want a relationship where they're the guy, and she's the girl and they have different hobbies. That's the only reason I can think of.
Ah, and I once heard, "You play games? ...Lesbian."