I'm very confused by the fact that this page itself does not have a visible focus style on interactive elements, making it very difficult for somebody who navigates the web with a keyboard to see what they are clicking on. I could not tell even if all the links on screen were actually reachable by tab key.

Maybe I've missed the point, but there are people who use they keyboard exclusively when navigating a web page already, and I would think accessibility for those people would be a big consideration in what you are doing.