4. Use The Fact You'll Have Different Reasons To Play The Same Game
This applies to most games but is possibly most easily explained in MMORPGs. Games such as World of Warcraft and the Old Republic have been known to get all sorts of gamers from all walks of life involved from all around the world. The idea of questing with a party in Azeroth who in reality may be from all corners of the Earth is one that has much appeal to gamers and has famously led to friendships and relationships beyond the 'walls' of these MMORPGs. So if people all around the world can find common cause to raid a castle in Azeroth, there surely is enough in common between you and your girlfriend to do the same. World of Warcraft might appeal to you for its deep immersive environment and its role playing attributes, but your girlfriend may be in it more for the looting and gaming in itself. Neither of these things are wrong or lesser reasons to play the game, or that gamers with one primary set of motivations can't mix with another. In fact, an environment where people have some different perspectives on things can only be a good thing, and allows people to gain more out of these games than they otherwise would with a band of more similar minded folk ( after all, they are called Massively Multiplayer Online RPGs for a reason...). Sometimes, a bit of difference is a good thing.