Is this a first party controller? I have a switch compatible 8bitdo controller which works but controller input is pretty much voodoo on windows.
You might be able to use steam input somehow. If you add it as a non-steam game.
I ended up using my keyboard to play the game using a program called ControllerEmulator by Relics97! My controller is called "PDP Faceoff Premiere Wired Pro Controller for Nintendo Switch", it is a licensed third party controller as you might guess. Either way I loved the game a lot, I'll write a bigger review on the submission page!