Sokal was right, of course. He deservedly made fools of a bunch of naked emperors. However, he also influenced a lot of people (myself included) to eschew a whole genre of thinkers for which there was a lot of truly brilliant ideas.
For example, Lacan is given a good spanking by Sokal both in his paper Transgressing the Boundaries and an entire chapter is dedicated to him in Intellectual Impostures. Lacan looks like a complete fool if this is your only exposure to his thought. Again, Sokal is not wrong on his criticisms in these excerpts. Lacan definitely uses mathematical terms incorrectly. He was making an attempt to formalize his field (psychoanalysis) by skimming textbooks/papers on topology, knot theory, and other mathematical subfields and, from the perspective of someone who uses those terms for precise things, rather haphazardly putting them together. His "mathemes" go through many updates throughout his career, getting ever more complex. Later, Lacan almost certainly was suffering from senility (as most of us will by age 80), and got rather obsessed with the fake math side of his own work.
However, if you actually read Lacan, this is a miniscule and often completely ignored side of his work. No Lacanian psychoanalyst is filling their notebooks with fake math formulas and computing what's wrong with your relationship with the objet petit a. They're metaphors, shorthand, or diagrammatic expressions of what he's really saying in the ~10k pages of his massive corpus. Many of us use compsci terms all the time to express things metaphorically (e.g., being out of bandwidth or disk space when we really mean real world time and mental memory). Think about it this way, and Lacan becomes a source of manifest brilliance, as I discovered only way later in life.
All that said, the critical theory and cultural studies space of the 90s was indeed a cesspool, living in the shadow of former intellectual greats. The great flood of mediocre intellects was starting to bear its rotten fruit, but the truly fatal problem was the politicization. Sokal only addressed this some, making surface-level wrongness his focus in some kind of defense of his own field's purity. Politics poisoned critical theory just like it did wherever else a field became subservient to the street-level goals of a political monoculture. Mindless foot soldiers, bleating about race and gender, capable of only bumper-sticker-length thoughts, make poor philosophers, it turns out. That should've been the core of his point, and could've been helpful framing for a countercurrent against it. Leftist intellectuals, or what was left of them, could've cleaned up their own space, and put the people like this article's author in a quiet corner where they belong. (Note how even here, he can't help but get sucked into the immediacy of the left-reactionary political zeitgeist; the spittle being anything but subtextual.) Instead it came to its inevitable, expensive conclusion of having the decolonization of the university from political imperialists done for them by their equally unthinking opponents.