Sports do not in any way make you stupid or decrease the amount of time you spend studying. That logic would only be valid if every single person spent all the time they have after school and on the weekends studying. The only factor that has a longterm effect on time spent studying would be the persons motivation to do so. I would argue most gamers study LESS then the general population.
Also studying is not a measure of intelligence. It might help you do better in school, but really school marks are no measure of intelligence either. School at its core is simply the art of memorization and calculation, it has little effect on your ability to think logically, fluently or your ability to solve problems presented to you without prior explanation.
And as thorax said, many gamers are physically fit and do play sports, myself included. I've been in hockey since I was 11 and at no point did it impede on my ability to study for tests and such.