I'm a psychologist whose research is close to this area. (Maybe in this area?)

The Quora post is kind of a trifecta of topics that tend to elicit very internet-y types of controversies for lack of a better way of putting it.

I can't speak for Peterson, to provide some context, I can understand where he's coming from. There are researchers of all sorts of backgrounds who spend a fair amount of time studying empirically the contours of human behavioral and psychological individual differences, and there are certain ideas that come up in the popular discourse, and persist despite their being a scientific literature that speaks against them in one way or another. They resonate with people because they do have variously sized kernels of truth to them, but somehow the scientific literature never gets injected into public discourse. This eventually feeds back, though, in textbooks and standardized exams, and it's like you're constantly fighting a battle for precision of terms.

Here's a small sampling of things that will trigger a response like that of Peterson on Quora: EQ, grit, Myers-Briggs.

The new MCAT is an example of this--the behavioral sciences section is horribly outdated in certain sections. I'm not sure how it got the way it is. But it's a major test, so now you have to teach to it, which then leads to a distorted perception of psychology and behavioral sciences by who are interested in the biomedical sciences, which then leads to all sorts of strawman arguments, and so forth and so on. It's like if the biology section included a section on intelligent design or something.

Anyway, the problem with something like EQ is that yes, there are non-cognitive determinants of success: empathy, social perceptual skills, perseveration, conscientiousness, socioeconomic background, and so forth and so on. So EQ captures this vague idea that IQ isn't everything.

The problem is that saying "IQ isn't everything" doesn't mean that a construct like EQ, which basically means "non-cognitive traits", is empirically precise and contributes something meaningful above and beyond other constructs mentioned by Peterson. These kinds of discussions create problems, because they create this false sense that if you argue against EQ, you're arguing against the idea of non-cognitive determinants of functioning, or arguing that IQ tests can't be improved, which is a false argument. Rather, what Peterson is saying is that there are well-characterized constructs like Big Five Agreeableness, or Conscientiousness, which have demonstrated predictive validity, and that are empirically coherent and precise enough to be more-or-less workable for lots of theories. That doesn't mean you can't be more precise; it just means that they represent a certain baseline of precision.

Contributing to this a certain confusion about what's meant by "thingness" in these literatures. Behavioral scientists are often studying actions, states, experiences, which are not physical in the sense of being objects (even though supervenience holds, so physical things underlie them), which is a little more abstract than what people are used to thinking about. So there's predictably some offshoot discussion about that issue. It's a bit like arguing that DL nets aren't things because they aren't instantiated directly in neuromorphic chips.

You're right to be critical of the idea that IQ is everything. But I can see where Peterson is coming from in certain respects.