Oh, I didn’t think itch.io app requires to package games in such way. I actually use
butler for all my games and it does exactly that. But it packages everything in a
zip archive, and those commonly store everything at the top, so it won’t surprise anyone.
In that case you could use
zip for the Linux version as well. Or give
butler a try, it’s actually a very nice way to manage itch.io releases. ;-)