The way it worked is that someone nominally representing the CA State Government had* ca.us, and they in turn gave* san-jose to someone who nominally represented San Jose, los-angeles to someone who nominally represented Los Angeles, santa-cruz to someone who nominally represented Santa Cruz, and so on. city-name.ca.us domains were still free (and charging for .com and .org domains was a new thing at the time); you would look in the zone file to see who owned* a given domain, email them with your nameserver names and IP, and they would add it to their zone.

This isn’t how things are done these days; names visible to the public are pretty much always in the form {domain}.{tld} or sometimes {name}.{domain}.{tld} (e.g. my own https://samboy.github.io). Registration is now done by bots and companies that spam you to death to try and get more money from you (the Internet wasn’t like that in the beach.santa-cruz.ca.us days). Domain names with multiple levels of delegation aren’t around they way they used to be.

* rented/leased/had control over/whatever

> This isn’t how things are done these days

The old locality domains still exist, and in many localities you can still register them today by the same "email a request to some sysadmin" process. https://news.ycombinator.com/item?id=48122635

Your beach.santa-cruz.ca.us domain is still in DNS, just with a broken delegation chain. You could reclaim it right now by setting up a nameserver at reality.samiam.org.