Unfortunately, there are some issues between the Unity Engine and the pro controller. I haven't been able to get it to work myself.
Steam interferes with Nintendo Switch Pro Controller input - so maybe try 2 things:
1. Close Steam before running the game.
2. Add the EXE as a Non-Steam game to Steam and boot through Big Picture mode. If you go to controller settings, you can turn on Switch Pro Controller Configuration, which will trick A Short Hike into think it's an xbox controller.