HTML is the correct choice here. You'll have to upload a ZIP archive, 'cause otherwise how do you plan to get dozens or hundreds of files at once on the server? The archive you select to be played in the browser won't be available for download; you'd have to provide a separate one for that.
If what you're saying is that people must go to the game's website to play, that's another story. You could upload a webpage that embeds your game in an iframe, for instance. But Itch doesn't directly support that kind of thing.