Earlier quoted context omitted.
This is not correct. The TLD alone is a valid domain name, although in most cases it must be followed by a trailing dot. "ai." is valid, "ai" may not be.
It is a valid domain in the technical DNS sense. But practically speaking, each TLD has "ns" entries in the root zone database, not "A", "CNAME", etc. entries. This is just a guy who registered www under a TLD that's it.
$ host "ai."
ai has address 209.59.119.34
ai mail is handled by 10 mail.offshore.ai.