The normative claim is one I am making now about the 'rationality' theories in question.

I quoted badly; I believe there was a misunderstanding. The first quote in the parent to this should be taken in the context of your sentence segment that "Said literature gives advice". In my paragraph, I was objecting to this from my experiences in my course, where I did not receive any advice on what to do in games like PD. Instead, the type of advice that I received was on how to calculate Nash equilibria and find SPNEs.

Otherwise, I am mostly in agreement with the latter part of that sentence. (ETA: That is, I agree that if current game theoretic equilibrium solutions are taken as advice on what one ought to do, then that is often epistemically, instrumentally, and normatively bad.)

More ETA:

conditional on confirmation from one of the Vladimirs that the axioms in question do, in fact, imply the faux-rational (CDT like) conclusions the term would be used to represent. I don't actually see it at a glance and would expect another hidden assumption to be required.

You are correct – VNM-rationality is incredibly weak (though humans don't satisfy it). It is, after all, logically equivalent to the existence of a utility function (the proof of this by von Neumann and Morgenstern led to the eponymous VNM theorem). The faux-rationality on LW and in popular culture requires much stronger assumptions. But again, I don't think these assumptions are made in the game theory literature – I think that faux-rationality is misattributed to game theory. The game theory I was taught used only VNM-rationality, and gave no advice.