The thing is, even when parsing html "correctly" (whatever that is) regexes will still be used. Sure, There will be a bunch of additional structures and mechanisms involved, but you will be identifying tokens via a bunch of regexes.
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.