Popcap Games might be a good step in the direction you seem to want to go. Sure, they may reek of casual to you but it's moving her away from facebook games. None of us became social lepers in a day and your girlfriend won't either. From Popcap you can lead her closer and closer to what you consider proper games.
Then you spring 'Ninja Nazi Slaughterfest XIV: Gore Nation' on her!
Then you spring 'Ninja Nazi Slaughterfest XIV: Gore Nation' on her!