When I click Install it just downloads the installer to C:\Users\<username>\AppData\Roaming\itch\apps\super-win-the-game\ and when I click Launch it just opens that folder in Windows Explorer.
I've run the installer myself and it installs the game and it's playable but the itch launcher (and thus Playnite, which is what I primarily use) have no knowledge of the actual install location for the game and I don't see a way to manually override the action for the Launch button in the itch launcher.
This may be more so a problem with the itch launcher / process but not sure where else to post about this issue.