It is by no means weird. It is absolutely cool for girls to like video games. There are not much of a difference with what girls and boys like these days. It should not matter one way or another if girls like or play video games.
I am a 32 year old girl who started playing video games around 1984. I collect systems, games and game related "stuff". If that makes me weird then I guess I'm weird. I don't know of a lot of girls who share my enthusiasm that's for sure.