Unfortunately there's no explanation which means there's no science here. (The world seems to be full of studies which measure things that are easy to measure and say things that people want to hear.)

Here's an explanation as to why exercise might be good for you: exercise transfers attention away from repetitive thoughts and into one's body and one's surroundings. It thus confers benefits similar to those of meditation.

This theory may well be totally false. But, hey, at least it offers an explanation. There's something there to be false.

The next step would be to criticise the theory and then, if it stands up, to test it against current theories.

Any testing though, would be highly unlikely to resemble the observations referred to in the linked article. It would instead depend on the relevant details of the rival theories.