Or they could find some way to legalize the chess-playing so that it's no longer an infraction, no longer a broken window, hence no longer a prelude to more crime. They could redefine the "kid's park" to exclude the chess tables, for instance, so the rule did not apply there.
But honestly, I think the "broken window" reasoning has nothing to do with them breaking the rules and more to do with class. A lot of the chess players are poor, some of them are street people, and a lot of the ones who aren't poor look and dress like the ones who are. The parents look at them with a certain prejudiced eye and think, "These people are not a wholesome element, they are of the street." And the parents fear that criminals and junkies might look at the chess players with the same prejudiced eye and think, "These guys are of the street; they're poor and low-class like me. If they're welcome here, then me and my criminal behavior are welcome here too." So the theory is that parents will stop bringing their kids, and low-grade criminals will start hanging out. Because of the perception of the chess players as a "street" element, basically a conflation of class with criminality, their presence can turn a park sleazy through no fault of theirs, just through the prejudice of other people. And some instinctive, gut-feeling version of that theory is what resulted in the police being tasked to "clean up" the park by evicting the chess players.
That's unfair. Innocent people shouldn't be punished because of how they're perceived by other people, even if that perception is causing real harm.