I have installed this game after a very long time and after its installation I discovered that GFWL has been removed from Batman: Arkham City and the game has now been transferred to Steam.
In addition to purchasing the game, I also purchased all its DLCs from the Games for Windows Live website (spending around $35). I own Batman:Arkham City (GFWL Edition) that I purchased from a retailer back in December 2011.