Just tbh: I personally would like to say thank you for the amazing artworks you did! I follow you on instagram since March/2023 when I started playing around with blender, I did some liminal stuff too but you make the greatest ones. (my profile is @dr3am.stack)
To export the game nativelly on Linux you need to use a linux system for this, like Ubuntu, Manjaro, Debian, etc.
Then with UPBGE and Blender installed on it, you go to compile as game, but will be there a different option, "for linux".
You can do it through a virtual machine with VirtualBox, maybe take some time to export but to just export it will use the CPU, maybe there is no problema. Another point: There are some caveats when exporting a game on another system, some adjusts maybe need to be made.
If there is no problem for ya, you can host the source files of the game so I can download and I can compile it for Linux. I use linux as my main system and I did some things on UPBGE in the past, I can help you to improve the game too. Would be a pleasure and such a honor to help one of my favorite artists!