I guess that the dev did use that download button "creativly". I recently did saw an external link that did open the download dialog of the browser directly. But most of the time it is just the respective file hoster's page that opens.
There is no payment active, but if it were, itch would expect the download button to lead to an actual singular download. But even without payment, it is a statistic thing. The dev might have a counter of downloads from itch. I do not know, if the dev could distinguish from where the traffic comes, if the files are on a file hoster.