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And that is where it makes the least sense. Why are downloads blocked when there aren't payments, but with those that have donations there is no problem?

could be that the monetized games get put on the "good" server 'cause Itch.io gets a cut of that money and therefore has an actual incentive to make sure everything works

If it were server side, it would not work on other browsers. Also, did you try what I wrote? The game is not blocked. FF thinks it is a page to display and not a file to download.