Actually the app is designed to work in a specific way, but it won't properly function if the developer doesn't do something.
That specific something they have to do is label the game download as being made for a specific system. In this case, Windows.
The Itch app won't let a Linux user download a Mac version of a game, nor will it allow a Windows user to download an Android APK. It will only allow you to download versions that are compatible with your system.
Since the dev hasn't labeled the download as being made to work with any specific system, the Itch app just assumes it won't work on your system and doesn't let you download anything.
This is a quick fix for the dev. All they need to do is correctly mark the download as a Windows executable.