I'm using a Logitech Rumblepad 2. Yes I did try the d-pad, but no response. The analogue stick works for the game, but the button mappings are a bit different. It could be an incompatible controller issue...
In any case, I'd like to learn more about how you made such a great looking game in Unity. You've listed the asset store packages used in your end credits. It would be great to hear more about your art creation and lighting process also. Thanks! ^^