If itch.io is having problems try downloading directly from StarshipInanna.com, but I can't seem to find any link issue with itch.io or any problem with the downloads through here.
The only thing it might be is that some browsers consider it a pop-up to download through itch.io and is blocking the pop-up (and some browsers do not tell you all that clearly) this is because the game is too large for itch.io and is hosted on our servers.
I can't explain it either, but if I go into incognito mode and try and download it throws up a blocked popup (even though all we're essentially doing it hotlinking from the itch.io site to the download on starshipinanna.com) I would imagine that most games on itch.io are small enough to be hosted internally, SI has a lot of art and music in it and is just going to grow bigger (I will admit I have not checked if the current version of the publicly available game (where we compressed the images and the audio) is withing the itch.io limit, but earlier versions certainly were not.)