Do I Have a Right? is the best example I’ve run across of game-base learning. It uses elements of resource management games like Diner Dash, but instead of giving patrons the correct food, you must direct them to the proper lawyer who can address their constitutional problem. For example, an NPC may come in saying that she was told she can’t vote because she is not of drinking age, but is 20 years old. You would need to direct her to a lawyer who knows the 26th Amendment. Similarly, you might get a buy who comes in complaining that nobody will pay him to be an actor. You would need to let him know that you can’t help him since there is no constitutional guarantee that you be paid to be an actor.
I can imagine a version of this that might be used to teach various aspects of Christianity. An NPC might come in with a question about Jacob and the player would need to direct the NPC to an Old Testament scholar, or an NPC might come with a question about Baptism and being buried with Christ and would need to be directed to a Pauline scholar.
If you know of any other games that impart knowledge as a core part of the game, drop me a line on twitter @byamabe.