like all things, the answer is both yes, and no.
Am I playing a Sport when i play a pick up game of basketball on my driveway, or running a mile in my neighborhood? I'd say no on both of those, as there is no real competition. However, if I am in a league of some sort, or a tournament or something similar, it becomes sporting, or running in a track and field competition then running a mile is a sport.
The same can be said of Chess or poker, or Boggle, or Scrabble, or checkers (Just to point out... the person who said that chess is WAY harder than checkers hasn't done their research. There is almost as much theory on checkers as there is on chess). If I play a game of chess with my dad in my living room, I do not believe that I am playing a sport. I'm playing a game, but if I go to a tournament then I'm playing a sport. Its about the competition first and foremost.
I think most people cannot grasp that athletics and sports are two different things, because the two terms have been used synonymously for so long, but they are not.
Just one more thing: If all sports require physical exertion, why then, did I double letter in both debate, and academic team in high school?