I Had a lot of trouble getting this working, but I think I have everything figured out. My laptop is running Fedora 41 KDE Plasma spin, so I can only say for certain it works on this distro. If this doesn't work for you, hopefully it helps you get on the right track.

For the game itself, easiest way to get it working is to run it through Lutris. It's great for getting pretty much anything non-steam working. Go to add a game, add a locally installed game, and select the appimage. For me it just worked. From here on will be mild spoilers.

Files that should have showed up in documents were just in ~/Documents/ for me. (You might want to make sure you have a ~/Documents/ directory though). At one point it will try to change your wallpaper, this didn't work, but the image is supposed to be this. https://imgur.com/LrZjaWR

Later on, a folder will show up in ~/Documents. There should be a .desktop file in there that also refuses to run. Open it in a text editor and locate the file it's pointing to, it should be ~/.local/share/Oneshot/_______. Add this file to Lutris as well, but this time go to the system options tab. Scroll down to environment variables, and add a new one. Set key to 'QT_QPA_PLATFORM', and value to 'xcb' (without quotes). Now it should run. 

Everything else from here worked fine for me, including the 'extra' stuff after the ending, so hopefully this is enough to get the broken linux port working!