My experiences with girls that play games has been as mixed as my experience with guys that play games. Some are intense, while others are calm; some are great at games, while others aren't. I do wish there were more girls that played games, though because whenever I tune into video game tournaments, I always get excited when girls clock guys in games. Sort of like how I will be all jittery if Hillary wins.
My experience has been largely the same.
My cousin is a girl who plays games. She loves JRPGs (Kingdom Hearts is her fave), the FF series, Persona, all that good stuff. Super duper calm, and really good at games. But I know this other gamer girl who is super duper intense, not as good at games (couldn't beat Donkey Kong or The Wonderful 101), and spends most of her time screaming at Dota 2. Girl gamers come in all shapes and sizes, and I greatly appreciate anyone who can appreciate video games.