That sucks because I don't think I've ever had a friend who's a girl who doesn't suck at games.
Traditionally serious gamers are fat and lazy, but games are changing and with that so are the gamers. Everyone I know plays some game. A friend of mine is a football nut, he only plays Madden and Socom. Another friend only plays iPhone games when he's bored. But the kind of gamer that goes to ComicCon or waits outside EB for 6 hours for the next Warcraft, they're mostly still fat and lazy with questionable hygiene.
As for girl gamers I've only ever known one girl that played video games. She never played on her own though, we played Minesweeper flags over MSN and Midnight Club DUB Edition on my Xbox. I could have beat her with one hand in Midnight Club but she would absolutely slaughter me in Minesweeper flags no matter how hard I tried. We both went easy on each other and we both knew it. Every other girl I ever met thinks video games are dumb. And that's where the stereotype comes from, most guys play games and most girls don't. Obviously someone who doesn't do something will suck at it.
Most are. And like 70% of the rest of the western world is fat and lazy--and that combined accounts for like 90% of gamers on the planet.
As for the girl gamer thing, well I suppose I'm biased, but that's one stereotype that I hate. I admit, FPS games are not my forte, but I AM good on RPGs. On the otherhand I have girl gamer friends that are pretty awesome on shooters, one has a gamer score of over 10,000. Go figure.
Biggest pet peeve: "lol thur are no girlz on teh intarwebs lol". Yeah, hi, I'm a girl with an internet connection. Do you deny my existence? Yes? Alright, tell me if my fist in your face feels real. Can you do that? *punches newb*
Unfortunatley stereotyping is one of those things that no group will go without, and they will probably never be dropped, so the best thing to do would be to just completely ignore them.