Katzapult: Well, it actually mentions controller support. But that´s not solving the problem. Sorry. :(
LOL I just looked and noticed that he didn't mention which game he was trying - but the gamecard I peeked at DID mention controller support.
HOWEVER it said it didn't support TWO controllers - OP, do you maybe have a second controller plugged in? Like a flightstick or some sort of different device?
Maybe pull out any other devices (obviously leave your keyboard and mouse plugged in) and try your 360 controller in a different USB (sometimes mine likes to be in the snazzy USB 3.0 ports up front). You said your controller works with Steam games, so I'm assuming if you're using a wireless 360 controller you have your dongle and drivers set up.
Also, make sure the controller is plugged in before the game starts. If that doesn't work, plug in the controller AFTER you start the game (oddly enough I had issues with The Saboteur this way - 90% of the time you want that controller plugged in BEFORE you run the .exe - Saboteur the cursor would fly all over the screen unless I started the game and THEN plugged in the controller - weird!).