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Bundle_Gerbe comments on Game Theory As A Dark Art - Less Wrong
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As far as I know, this version is a form of prisoner's dilemma: Payoff(C,D) ≤ Payoff(D,D) < Payoff(C,C) < Payoff(D,C). Normally, Payoff(D,D) is > (strictly greater than) Payoff(C,D), not just (equal or greater than), but it's still reasonable to call this game a weak form of prisoner's dilemma, as they share most characteristics.
Nothing to say here, but I apparently have to put a "2." in if I want the "3." from below to be represented properly.
Technically you're right, though in this world of evolution and repeated social interaction, Nick did change the game by gambling not alone with money, but with his trustworthiness as a benevolent human being as well. Nick would look like a total douche to most people who get to know what he was doing, including his friends and family, if he chose steal and took the money all for himself. By making the air pressure oscillate in a certain way, Nick made it long-term unfavourable for him to steal the money completely, so the best he could do from there on was probably to either split or to steal and then split. From this perspective, he in fact did change the payoff function.
The specific problem with calling the last game a "prisoner's dilemma" is that someone learning about game theory from this article may well remember from it, "there is a cool way to coordinate on the prisoner's dilemma using coin flips based on correlated equilibria" then be seriously confused at some later point.
Of course, by changing the payoff matrix, Nick also changed the game, so after him putting in some more of his stakes, it wasn't Golden Balls / PD anymore but a game which had the structure Nick favoured. What is to be learned from this article is how to design games to your own profit - whether you are watching from the outside or playing from the inside.
Apparently I didn't quite understand what you wanted to tell me - I'm sorry! Yes, as an introduction to game theory, this indeed is a problem. Example #6 is a bit out of place for that, as game theory here didn't work in practice in the sense that it didn't make accurate predictions.