Oh, I've just re-read your original message, perhaps I should confirm there is a difference between the initial "download" button and actually downloading the files. Its a very badly worded button in my opinion. You have to click on the first "download" button on the download list to add it to your library; you don't need to download the actual file, and it doesn't download a file - it provides a list of available files on the next page. e.g. you might might not use those, and use the itch.io app instead.
It would be far better if that first button was called "Add to library", not "download". Would save so much confusion!!