I don't have a linux machine to test on, but it sounds like it really is just extract the TLHE rar, run the Game.exe, and it just works. Have you tried deleting it, redownloading, and trying again from scratch?
What Linux distro? Is it a gaming one like SteamOS or Nobara, or something else? I'm not sure why I ask to be honest, I don't have any insight based on distro. Hm.
Oh. I know another user that is both adept on the topic of Linux and about RPGmaker on Linux
specifically. He does those ports for MV and MZ games to Linux. It's
m4kro
Maybe he can help you out with the specifics.