Hi, glad you enjoyed the demo! The full game actually has compatibility for more gamepads. I haven't updated the demo for quite a while. Other gamepads that didn't work in the demo now work in the full game.
Also I am working on an update for the full game where you will also be able to use point-and-click movement to navigate, very similar to The Search. It might be another week or so before that update goes live though.
Either way, if the gamepad doesn't work you could wait until the update for the point and click movement. You could refund the game too if none of that works. ;-)