No the main reason why that happens is because he checks what systems are avaiable and if windows is not listed it just wont download it and say its unavaiable
You you are unable to download any file? I know other itch users have gotten access to it. I do not know if they are using the app or not though. I am sure if you went through without the app you would be able to grab the file. I will look on my side, perhaps you want to post to itch and see if this is a problematic case. For if it is as you say, then the app will not work.