From https://en.wikipedia.org/wiki/Webring :

To be a part of the webring, each site has a common navigation bar; it contains links to the previous and next sites. By selecting next (or previous) repeatedly, the user will eventually reach the site they started at; this is the origin of the term "webring."

But, it was a fundamentally silly structure for the web, so many sites implemented something beyond the ring structure, which is what you're describing. Technically, those weren't webrings in the above sense.

It's "ring" like a boxing ring

Nice retcon, but wrong.