Learning games have a different primary goal from entertainment games, and it's an open question whether the two can be completely combined or if they really must follow separate rules. Below are annotated links to learning games, videos of learning games, and readings about them.
Amplify.com has developed several games to supports its Common Core curricula. Here's a 3-min. YouTube video that describes their games as of Summer, 2013: http://www.youtube.com/embed/SPG-6F19ETU.