Via Steam,
Installation
since steam enables proton by default as of July 4th/2025. you don't need to do anything other the click "install".
Getting it to work
once installed, you will notice it doesn't run so head to your files.
in your "Home" folder, press CNTRL + H to show hidden files and it should look something like so:
Then you need to head to this folder nestled inside to get things working:
The real game comes in two variants: Battlegrounds.exe is the basic game, and battlegrounds_x1.exe is the basic game plus the clone campaigns.
You need to remove or rename player.exe and replace it with either of the two above mentioned .exe files.
in this instance, "battlegrounds_x1.exe" was copied and pasted with the right mouse button "copy" then right mouse button again "paste" then once last time to rename it to "player.exe."
And your now done!
Open steam and hit play!!!
HUGE CREDIT to Almos on steam for his post, it expands on this as the original fix required a few extra steps and also show him some support for figuring this out.
Tested on Zorin OS/Cachy OS/ Linux Mint and confirmed to function.