In fact, not all the options require download. If you look around, you'll notice we have a lot of browser games. If you select HTML under Kind of project, you'll be able to mark a file or archive you upload a being playable in the browser, and you'll get all kinds of options as to how your game will be loaded.
Now, if your game is multiplayer and hosted on your own server, then no, you can't just place a link to it in a text field and call it a day. But you could, for example, create an index.html file that does nothing except embed your game in an iframe, and upload that to Itch. Hope this helps!