I'm sure you already know this one, but for anyone else reading this I can share my favourite StackOverflow answer of all time: https://stackoverflow.com/a/1732454
Guy (in my reading) appears to talk about matching an entire HTML document with regex. Indeed, that is not possible due to the grammars involved. But that is not what was being asked.
What was being asked is whether the individual HTML tags can be parsed via regex. And to my understanding those are very much workable, and there's no grammar capability mismatch either.
So yes, while it is an inspired comidic genius of a rant, and sort of informative in that it opens your eyes to the limitations of regexes, it sort of brushes under the rug all the places that those poor maligned regular expressions will be used when parsing html.