There are a few things going on with this quote.
The quote is a restatement of an earlier joke:
Whenever faced with a problem, some people say "Lets use AWK." Now, they have two problems. — D. Tilbrook
It is a joke and a real dig, but it's also a way of highlighting regex as a bad solution by linking it with other bad solutions. It's a great ha ha only serious moment.
To me -- mindme—mind you, this quote is purposefullypurposely open to interpretation -- theinterpretation—the meaning is straight forward. Simply announcing the idea of using a regular expression has not solved the problem. In addition, you've increased the cognitive complexity of the code by adding an additional language with rules that stand apart from whatever language you are using.
Although funny as a joke, you need to compare the complexity of a non-regex solution with the complexity of the regex solution + the additional complexity of including regexes. It may be worthwhile to solve a problem with a regex, despite the additional cost of adding regexes.