The public build isn't marked on Itch's website as being compatible with any OS, which means that the itch.io desktop client doesn't realize that it's an installable program (meaning that a standard web browser has to be used to install the game instead).
There should be a section on the page for the download's properties that looks something like this; ticking the boxes for Windows, Linux, and Mac should let the itch.io desktop client know that your download can work with those platforms.