If your Buffalo SNES Controller is not behaving correctly with with this game, changing controller support options in Big Picture mode may fix it.
Big Picture Settings
This is a very simple fix for a specific problem I've had with the Buffalo SNES controller, which is known to have phantom input issues. I think it may even fix this issue across all games on Steam. I've seen other fixes for this that involve running scripts or opening up the controller itself and changing out capacitors, but who wants to do that!
Go into Big Picture mode, enter Settings, and select Controller Settings. Set the controller support option to "Nintendo Switch"
That's really all there is to it. When I first booted up this game, the Up arrow on the d-pad kept activating even when I wasn't touching the controller. I had the same problem with Undertale, which leads me to believe this should fix all Buffalo input issues with phantom presses on the d-pad.
Remember to change the controller configuration back to your main controller of choice if you want to play 3D games again. I'm sure that not doing so could cause some unforeseen issues.
Let me know if you have any deeper knowledge about this so that I can amend this guide so that it doesn't lead anyone astray if it does not work for your input problems.