It appears that paper has nothing to do with kids who have been diagnosed with ADHD... at least there's no mention of that in summary unless I'm really missing something. The article in the Atlantic cites other work that is ADHD-specific.

This is important because it is not uncommon to find interventions (including drugs) that benefit people who do not have a given condition that do nothing for people who have the condition.

To take a ridiculous but hopefully memorable example: steroids will not help a person with no arms lift more weight, even though they may help other people a lot. In the case of metabolic diseases, sufferers are generally missing important metabolic pathways that the rest of us have, so the example isn't completely irrelevant.

In the present case, I think it's perfectly reasonable that exercise will help (although what I think is perfectly reasonable and what is true have nothing to do with each other) and as the Atlantic articles says, other studies have shown this, but I just wanted to make a pedantic point about that particular pediatric paper.

The study says "The exclusion criteria included special educational services related to cognitive or attentional disorders ...". So kids diagnosed with ADHD had been specifically excluded. This should be tried on ADHD-diagnosed kids. If they're physically healthy, 70 minutes a day of mild exercise won't hurt them.