That's really not the point of the article. He updates the A records for his home machine that doesn't have a static IP.

Pi-hole is a DNS resolver: it takes questions from clients, such as "what's the IP address for google.com"? And takes care of contacting an authoritative server (or passes it to downstream resolver, which does the work) to get the answer.

An authoritative server is responsible for answering that same question, but it's been labeled as authoritative for a domain, via the domain registrar system. To see what servers are authoritative for a domain, you can use commands like dig or host; here's an example host command (I'm running OSX, but this should work on any *nix that has it installed):

  $ host -t ns ycombinator.com
  ycombinator.com name server ns-1411.awsdns-48.org.
  ycombinator.com name server ns-1914.awsdns-47.co.uk.
  ycombinator.com name server ns-225.awsdns-28.com.
  ycombinator.com name server ns-556.awsdns-05.net.