The linked article is a complete waste of time as the authors don't bother to explain what the extortionate strategy is, only insist that it turns the game into an ultimatum. And the title must be a lie, since halfway through, it explicitly says TFT gets the same score as its opponent. (In other words, it doesn't get "beat" by anything.) So the parts of the article that are true are useless, the parts that are supposedly interesting are asserted, unexplained, and the title is certainly false. Downvoted.
There was a previous post about this topic that actually linked to the paper, which I think you'll be happier with.
In particular, what the extortionate strategy does is the following: if player 2 accepts that player 1 will play the extortionate strategy, and there's nothing to be done about that, then there is a linear relation between their scores, and he can only maximize his score by giving an even higher score to player 1. In particular, if player 2 plays TFT (which is also an extortionate strategy, in a degenerate sense, with extortion factor 1) then ...
Less Wrong had a Prisoner's Dilemma contest some time back, whose results I've forgotten. Perhaps it should be rerun with William H. Press & Freeman Dyson's proposed extortionate strategies.
I hope Pinker gives a response at Edge.org, since P.D played a significant role his book "The Better Angels of Our Nature" as a source of morality embedded in the nature of logic/reality.
Hat-tip to Marginal Revolution.