No of course not, in fact it doesn't even interest me much to have a girlfriend who plays games. Would be kind of nice I guess to have another conversation topic to talk about, but gaming is basically my alone time where I switch off for an hour and immerse myself in a world, so I very rarely play with other people. It's funny because I am a very social person outside of gaming but I am very anti-social when gaming merely because I consider multiplayer to detract from the fun of the reason I play games.
Also anyone saying 'she only need to accept me as a gamer', well that's fine, but I have to ask; perhaps you play games too damn much?? You shouldn't need to be accepted as a gamer, its just a hobby. If you need to be accepted as a gamer that means it has consumed you and become the biggest part of you, which frankly not only shuts you off from some great things in life that you're missing out on, but also makes you a fairly boring person.
Gaming shouldn't be your life, it's really not that healthy for relationships or your well-being.
Anyway each to their own, I guess, it's just my thoughts on the matter.