So I got it working? I ended up deleting all the game files manually instead of trusting Lutris to do it, and then reinstalled the game. It loaded and ran, then refused to recognize my keyboard or controller. I messed around with a bunch of settings, turned Bluetooth off and on, restarted the computer, nothing.
Gave up and went to bed.
The next day, got home and booted up my pc to give another crack at getting everything to work and…it worked just fine. I have no idea why. Yay #linux?