My interpretation of this for those with a bit of game theory background: Locality (in physics) can be translated (in game theory) as a constraint on correlate

My interpretation of this for those with a bit of game theory background: Locality (in physics) can be translated (in game theory) as a constraint on correlated equilibria, by pretty basic observations about Bayesian probability. Generally in game theory when you lift constraints on correlated equilibria you (weakly) expand the possible Nash equilibria. So one of their points seems to be that the quantum context (non-locality) allows for more (potentially better) equilibria. They don't emphasize applications of this, but one of them could be that distributed quantum systems could have better outcomes than distributed systems in the classical setting. (One way to analyze distributed systems is by viewing components as independent actors in a game.) There is also an identification between payoff functions and Bell inequalities, but I am not sure how profound this is really. It feels more like a technical point. Payoff functions are not terribly fundamental in game theory (compared to equilibria, for instance).