IIRC the old webrings had a CGI backend that would collect the addresses and then you would click "next" and it would take you to the next site. But yeah you could just make a vanilla one. You could also just make one outside of the context of Neocities.

But if the next site went down or didn't link to the next site correctly, you couldn't proceed. That was always my problem with webrings. They depended on each site to embed the ring code properly, and usually they didn't, so you were stuck trying to find a working one. It was a pretty lousy UX overall.