Here's nearly every newspaper article about science ever: "Until recently, scientists believed in $obviously_false_idea, but a recent study shows that..."
The idea that cooperation has been selected for by evolution to some extent is obviously correct, because otherwise we wouldn't have social species that can't survive without cooperation. It's also nothing new, it's one of the central themes of The Selfish Gene that everyone who feigns an interest in science pretends to have read.
I haven't read TFA, but I imagine the study was probably about some detail of how cooperation is selected for.
I have read TFA, and the paper isn't much like the news article at all -- or like the second part of the paper's title. The result is not a general result of "cooperation beating selfishness" -- indeed the algorithms they tested were out-survived by selfishness as well as being out-survived by cooperation. It's a mathematical paper, with a set of simulations, showing that a peculiar set of recently discovered stochastic strategies (ZD strategies) that have a curious mathematical property aren't evolutionarily stable after all. In the paper, ZD strategies are shown to be out-survived in a game of "prisoner's dilemma" both by selfish strategies and by (theoretically weaker) cooperative strategies.
But "this curious class of stochastic strategies you'd never heard of anyway turn out not to be stable in large scale multi-agent computer simulations of the prisoners' dilemma" makes for a rather less gripping headline.
The headline (and end of the paper's title) are spun from the fact that these quirky ZD strategies fail because they fare especially poorly in match ups against themselves in a population. But that is not a general claim that cooperation beat selfishness.