[gbacon]

Proving that a problem is NP-complete requires proving that it is NP-hard and in NP. Reducing SAT to regex matching with backreferences does the former. The latter requires proving that any solution can be checked in polynomial time.

The author is also incorrect in stating However the author incorrectly states that only 3SAT problems are solvable. Proof that 3SAT is NP-hard does not exclude broader SAT.

[dtech]

While not a formal proof, it is fairly obvious that verifying a match is in P. Just fill in the captured groups from the answer in the regex and see if it corresponds to the input text.

Every SAT problem can be converted into a 3-SAT problem so that's also not really an issue, they are both NPC