Is your project an executeable or is it a webgame (html5) or is it just a bunch of data files?
If you marked it as a webgame, despite being just a zipped folder and "a link" to your own website, you should change the attributes of your project to reflect that. (change type to download instead of html)
It sounds like you marked it as a web project, so you have to upload a zip file with the necessary items in it and a top file named "index.html" that will start your web game project. This would run on site without downloading.
See those twine games for examples. https://itch.io/games/tag-twine