When I try to run the game, it won't start.
Yep me too, I'm using the linux .zip file, on wine, I'm on Linux Mint x64, tried both, x86 and x64, it says loading input configuration, I select the resolution, press ok, then it shuts down :(
Sorry, I don't have a Linux machine so I can't troubleshoot. It was made in Unity, so perhaps the problem is universal to running Unity on Linux.
You shouldn't use the linux zip file under wine. You either use the linux zip file natively, or you use the windows zip file under wine.