I can download and play Buckshot Roulette, another Godot game, just fine so this must be some weird misconfiguration of something needed for the app, I suppose from your side and not itch.io but I may be mistaken.
I think I know what is different now, based on looking at the receipt.json of both games and comparing download files of Buckshot Roulette and this. You distribute it directly as .exe or .x86_64, while they distribute it in .zip.
receipt.json for your game reflects this, it tries to install your game "naked" while for Buckshot Roulette, it detects it is an "archive" as it is in .zip and just unpacks it.
Uploading the game in a .zip file should help this issue, would be appreciated! This is only game I have to manage myself via manual download... Not ideal when there will be some update.