1) Unpack the archive with a game or open the folder where it was installed by itch app;
2) Right-click on the x_86 / x86_64 file (depending on your system type) and select "Allow executing this file as an app";
3) Launch the app.
Possible issues with this app on Linux could be related to permissions, graphics drivers and maybe installing the Mono package. If the app doesn't work, I suggest trying Proton layer or Wine to launch the Windows version. There are lots of issues on the OS level that create issues for Unity apps there and it's out of my control.
I hope that it helped, thanks!