I don't think it's entirely analogous to that. The traits that he's saying are feminine are those that directly correlate to being less capable of securing higher wages. If someone is agreeable, they're less likely to be stubborn and demand that their boss pay them more, ultimately to their own detriment. But having curly hair doesn't make a person any more or less capable of negotiating higher wages for himself/herself. If someone was paid less because they had curly hair, I agree, of course it would be discrimination, because possessing that trait has nothing to do with one's ability to convince their boss to pay them more. But the argument here is that, in a free market economy, where people have to forcefully tell their employer that their labor is worth more than their bosses want to pay them, it's a disadvantage not to have a personality type that insists that they get paid more. It's not a matter of what one deserves, but what they are able to accomplish. And, according to Peterson's analysis (let's temporarily bracketing whether the analysis is correct or not) women disproportionately exhibit that trait, even if they don't possess it universally/by necessity.
He's definitely an advocate of the status quo, in the sense that he doesn't think government should step in to impose certain outcomes on the market (obviously, a person can disagree with him, and argue that it should -- at no point, I think, does he explain why its fair that disagreeable people should be paid more, except, I believe for that bit about "experimenting" with corporate structures built on feminine principles. Obviously governments can enforce equal pay through the law, and that could very easily be better than the status quo he defends). But he's also not saying that women necessarily exhibit certain traits, only that they're statistically more likely to exhibit them. I think it's worth bearing that in mind, when considering to what extent what he says he discriminatory or misogynistic. (Obviously, it's fishy that he's classifying more passive traits as feminine, even if both men and women can possess them. There's evidently a harsh judgment being made that feminine traits are inherently weaker and less effective -- really, worse -- than masculine ones, and that effeminate men are craven, pathetic people, destined to by ruled by manipulative women, unless they man up.)
I'm not quite getting this. He acknowledges that part of the pay gap can be attributed to outright discrimination. So it doesn't entirely conceal the role that the mere fact of being a woman plays (rather than possessing "feminine traits"), and, subsequently, that discrimination plays. Isn't it feasible that behavioral traits could be partially responsible for the pay gap, even to a significant extent?