Yes, it is keyboard only. In fact, glitches happen like no movement animation or sudden stopping when there is a controller plugged in. It's best to unplug the controller and play with keyboard. But I have seen someone find a way to use a controller for this and for HopBound.
Here is an excerpt from one of the steam reviews:
"The game doesn't have controller support, and even the developer wrote that into the store page. But I use a DS4 controller mapped partly to the keyboard, partly to the XB1 controller, and partly to the mouse using DS4Windows, and I am playing the whole game front to back using a controller only"