I'd love to put my new web game mystikaze.io on itch.io, but it is hosted on my web server so there wouldn't be anything for itch.io to host.  I'm a bit confused as to the nature of the content on itch.io - can I put my web game on here somehow or does it have to be "downloadable"?

Projects on itch.io can either be downloaded or run in a browser. I suppose you could create a page which links to where your game is hosted, but that may be against the itch.io tos.

Yes, you can put a web game on itch.io, there's explicit support for HTML5 games. To host the game on your website and only embed it here, you can upload an index.html with an iframe in it, for example.

Instead of iframing I used a meta redirect in index.html for my game