Webrings are still there, they're just implicit. People link within their content to the same resources over-again, or have more explicit footer blocks or aside link stacks.
Search engines use this structure for domain authority.
A search for "link:example.com -site:example.com" would have found that webring in the past.
Search engines use this structure for domain authority.
A search for "link:example.com -site:example.com" would have found that webring in the past.