Did you use Appimage format when you package your game?
I heard it's suppose to work on all Linux distros; I only tested on Mint and Ubuntu.
Viewing post in Any Linux gamers out there?
AppImage is useful for packaging, but it doesn't prevent broken builds by itself. I've seen plenty of Linux games without AppImage that work fine, and I think I've seen at least some AppImage games that don't work (although AppImage is pretty rare). I do use AppImage for my own games, but more importantly, I use static linking where I can and I redistribute .so files and use custom rpaths where I am forced to use dynamic linking.