I managed to rustle up an old laptop and turn it into a linux system. I've got Ubuntu Mate 20.04 on it. The game runs fine on it; however, the controller mappings aren't quite correct.
I was pleasantly surprised that the controller worked at all, and it is sort of playable, but the sensitivity is a bit much and there don't seem to be much of a deadzone on any of the axes. Also what LT and RT are doing isn't what they do on windows. Sorry, I can't be more specific because it keeps interrupting itself due to it trying to register too many presses all at once.
The vibration is working though, and you can still fire with A, just not RT for some reason. This is the same controller that I'm using on Windows. The only difference is that on Windows, it's connected via Bluetooth, and on this machine, it's connected via USB since the machine is 7 years old and doesn't have that capability.