Thanks for the hint! I'm still figuring out stuff with Linux. I'll see what possibilities I have in the process.
Happy to help you test things before publishing if that helps.
Unity3D (which I believe you used) has an option to spit out a Linux build, and can create a folder which contains your game data and two binaries, one 32-bit and one 64-bit. It means the player has to choose which binary to run, but they're running Linux so can probably figure that out ;)