> "Ring" means you are navigating linearly and circularly. Isn't it better to provide a list of links so users can choose where they want to go "next"?

That depends! If your goal is some optimal way of navigating, sure. But the shape of a webring means your site has two "neighbours", which is fun and uses spatial notions we don't see often anymore. It also means someone can remember Site Y as "the one next from Site X", which is also fun and creates more ways sites relate to each other. This relating to one another is usually the point of a webring.