Good news! We've had two reports of Linux users having trouble running the game, check out this one in particular.
Added a portable package for the itch.io app
Installing Zero-K using the itch.io app now works. We (foolishly) thought that the installer downloaded through the site would work the same way when using the app. We were wrong. Portable archives seem to be the way to go for the itch.io app so we have made a portable archive. For non-app users we recommend the installer as it will keep itself up to date.