No, it's that Bayesian players can take advantage of corellated quantum oracles in ways that give them acess to new equilibria in a way that preserves some of the old equilibria, such that the max of the new set of equilibria is always equal to or greater than the max of the old set. Which is rather non-obvious.

In addition, your statements "quantum-entangled systems can transfer information useful to game players" is wrong, or at least misleading. Entangled particles can't communicate information any better than classical methods. (Well, unless you're concerned about privacy, but that's a whole other issue which doesn't effect the game...)