Game theory is just math. As with any math, the calculations can all work out, but that says nothing of how it reflects nature. All you can say is that if the axioms are all true, then this is the necessary outcome. Look for string theory as a cautionary tale here.

Game theory assumes rational systems. But we have over 6 decades of behavior science which contradicts that fundamental assumption. Economic behavior is not necessarily rational, and subsequently it is not inherently game theoretic. You will find plenty of dogmatic, idealistic, superstitious, counter productive, etc. behaviors in an economy. You need psychology, and not just math, to describe the economics which happens in the real world.