I'd say the itch.io app is a rather "normal" way to play games on itch.io... Did it work when you tried it through the app? Do you use any antivirus that might be interfering?
So, does it work now?
You needed to extract it as that's how archive files work, if that was the question. They are just files and when you run Game.exe from directly from the archive it actually just extracts to a temporary folder on your computer in the background without extracting everything else and then runs, but as none of the other files around it have been extracted it just crashes immediately.