I’m not sure how the Itch app decides which file is the executable, but you can move all other files except the executable in the root folder, and hopefully Itch will recognise that as “the” executable?
Viewing post in Game won't run from app
Looks like the two Unity-packaged items the Itch app thinks are executables are irrelevant, although as I can't find any documentation on what they are I can't be certain! I can certainly fiddle things so my install script is either not in the way or runs the executable if called by the Itch app. So one way or another it can be fixed. Thank you!