"demonstrated exactly how intervention, rule-breaking, and destruction happen"? huh?
I didn't look up the explanation in New Yorker itself (because of paywall), but here‘s the next best thing I could find: https://uk.remonews.com/world-cup-2018-the-moral-clarity-of-pussy-riots-protest Which looks half-baked and unproofread (I would guess they have corrected at least some mistakes on New Yorker’s site). Apparently the extended version of the interpretation reads as follows:
"But the terrestrial policeman, who intervenes every day in the game and knows no rules, is destroying our world."
The four women, taking to the field, have shown exactly how this happens: the beautiful world of sport has its bubble punctured by people who run and agitate haphazardly, intent on destruction.
"exactly". A confused run in front of a frenzied crowd is, of course, an "exact demonstration".