I'm sorta trying to convince her to... My gf is not a gamer, and can be euphemistically referred to as being "not very computer-savvy", but she seems to have warmed up to the idea of playing WoW as a substitute for actually spending time together (in the past 13 months we only got to see each other for 2 weeks total, so yeah...) - something I already happily do with my other-other half, i.e. my best friend.
If we did get to spend more time together, or actually move in together, then we'd probably have more... interesting stuff to do. Plus, we both like to go Outside (it exists!) and play ball. Which can usually be more fun than gaming.
And actually, she has this distressing tendency to go "why play a game when you can do this in real life?" and proceed to do accordingly. Which is fine if I'm showing her a sports game, but if she does that after a bloody rampage in GTA...