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...)
> Entangled particles can't communicate information any better than classical methods.
Actually, with the aid of entangled particles, there's also superdense coding, which allows for two-bits-per-qubit coding (i.e. information density well beyond the classical limit).
Though I'm not sure what your metric for "better" is here, coding density seems to be mildly reasonable. OTOH, this isn't related at all to the article at hand, just a fun application of entanglement :D
I was hoping for some sort of nice link between the fields... like doing quantum mechanics with game theory or something like that. This appears to be playing a game with a quantum channel. Cool, but not that cool.
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...)