Not just because it's pro-social and non-rivalrous, there's arguments for this in game theory itself, in the iterated prisoner's dilemma it's often the strategies that start by cooperating and then fall back on competition that come out ahead when competiting in even good/bad actor competitions.
It's interesting that the original article even says this "Playing games and sports throughout life teach us all sorts of lessons about teamwork, strategy, pressure, practice, emotional control… I could go on."
I don't see any teamwork in chess, I guess there might be in poker (temporarily) but I assume there's only one winner at the end?
Our current culture seems to place most of the emphasis on competition, e.g. Education is all about getting better grades than everyone else and then we put people in workplaces and wonder why it ends up toxic?
Obviously you could argue that people being cooperative first would just lead to them getting exploited more but given we already have vast differentials in wealth, I'd certainly be interested in trying it out or what research on this shows?