Running your own DNS server doesn’t do much, unless your users are polling that DNS server, or a DNS server that pulls from it. No large DNS provider is going to honor your random ass DNS servers mappings, and that’s a good thing.
And honestly, trusting some random DNS server isn’t a good idea. All it takes is one malicious entry and https://google.com suddenly loads in a cryptominer.
I think he means he's running the name server for his zone (i.e. the authority for subdomains of his domains), which of course doesn't help if the top level domain gets suspended and the NS record gets deleted.
It looks like the registrar changed the nameserver, which is a harder thing to recover from. Still, didn't keep them down for long. Looks like they figured something out