What's wrong with you guys? I havn't seen any good advice yet. The question is how can you make your girlfriend sit in front of that computer, play for the first time and continue playing?
Girls love guys who are responsible and has a good work/ life balance. Make them feel that the game only comes second before her. Show them that you can still live your life the way it should be and not spend it just playing the game. When you go out with her, only 20% of your conversation should be about the game. If she's playing other games, life facebook games, try to join her once in a while and make it a way to communicate with her(just dont overdo it). Once you are ready to introduce the game to her, try to set a day where you are alone with her and ask if you can play the game. Make it look like you're enjoying it and give her an idea that the game can be a way to bond and communicate with each other. If she havn't seen the movies yet, it wouldn't hurt if you make her like that first. In any relationship, communication is the key. Use the game to communicate.
I hope this would help you out.