It came to my attention that if the user switches to the "Controller" input method inside of the game that the controller will not respond. Upon investigation it has been discovered that Steam controller management overrides game internal input methods when it comes to controllers.
This issue is now being addressed as we speak, as well as a handful of other little fixes and tweaks. Fix will be in place in the next weeks update.
Until then, you can use the "Keyboard" input method within the game and the controller should work as expected.