Amazon (Nasdaq: AMZN) is entering the game-making business and has unveiled a new department – Amazon Game Studios – and its first free Facebook (Nasdaq: FB) social-game title “Living Classics,” reports CNN. "Amazon Game Studios is exactly what it sounds like: a new team at Amazon that's focused on creating innovative, fun and well-crafted games," according to a post on the new site games.amazon.com. The department is hiring, but few other details are given, CNN said. CNN reported that…