I think that _initially_ this new neural growth can be co-opted into general mental flexibility, particularly for things like mathematics and visual reasoning. In a sense, varied movement makes you more aware/perceptive of space. However, I think over time if you don't try to utilize your increased spatial awareness to solve spatial problems, eventually those new neurons will prune their synaptic connections to make the network as efficient as possible. Thus, I believe that pairing novel mental and physical training is the best bet for improving overall intellectual abilities.

Short answer: yes, physical exercise has been scientifically proven to improve cognition (working memory, attention, and other factors).

In addition to physical exercise, the two other things the author neglects to mention (though it might not be as relevant for her population, comprised of children) are diet and stress relief.