Hi Th44r!
Thanks for playing and thanks for the feedback!
I'm afraid that at the moment you either need to unplug your controller (and then keyboard should work for everything) or exclusively use the controller for everything. We will add an option to disable controllers for those who wish to keep them plugged in. The Xbox controller is supposed to work and has been tested thoroughly. Perhaps try to unplug and plug back in while the game is running.
We will definitely add key binding in the near future!
Please let us know if you are still unable to play!