It is certainly true that correlation does not necessitate causation. However I do believe that, in this case, participation in recreational sport can - at length - lead to improved results in later high school years. I do not like labelling this improvement with statistics as specific as 2% or 5% though; his research would have needed to cover such a massive number of subjects for it to have a hope of being accurate. I don't think the score increase is any more direct than them being an off-hand result of the already scientifically explored benefits that an active lifestyle brings.
My basketball and the hour walk home I did from school every day kept me fit, healthy and happy. @ basketball I ran off my stress and got a huge endorphin boost. Even if it was merely an excuse to get myself out of the house, I enjoyed the human contact and the break from my studies. Any frustration I vented with a few extra fouls (which we shall not speak of XD) and running off all my extra energy made it easier to sleep @ night.