First up from Amazon Game Studios is a free game for Facebook users. Amazon.com Inc. this week launched Amazon Game Studios, a group charged with creating social games. Its first game, called Living Classics, costs nothing to play and is available only as an app on the Facebook social network. “We know that many Amazon customers enjoy playing games, and thanks to Amazon’s know-how, we believe we can deliver a great, accessible gaming experience that gamers and our customers can play any time,” reads a message posted to Games.Amazon.com, the home of Amazon Game Studios. The first game is a so-called moving object game, where players click on images as they animate. The Living Classics…