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Only Xbox 360 controllers and Keyboard are officially supported (as on descriptions on stores and inside "how to play"). 
Maybe JoyToKey could be an option in your case, but it's not officially supported.

Yes, JoyToKey is my mapping program of choice. Mixing JoyToKey and NON-360 controllers with this game creates a fantastic trio.
I should mention that, in terms of creating a clean and simple multiplayer experience, this game works really, REALLY well. And, the fact is, on this site, I only give comments to the best games, so... you shouldn't stress over the 360 controller constraints - they probably aren't your fault, although I am hoping that someday, the ability to disable controller auto-detection becomes a normal feature.

Sorry, if it's not possible to play this game with the gamepads of your preference :(

I believe this feature would be a nice one! But also could interfere for other player that just want to connect the Xbox 360 gamepad (or other xInput compatible) and play...

Thank you for your feedback and for your kind words. I'm really glad that you feel this way about this game :)