A couple of responses:
To the many people who said, "chess is physical because you move the pieces, so it's a sport," according to that argument, anything is a sport. Would you claim that eating, reading, or getting dressed are sports as well?
And to Cheater_1: I'm not sure that there is any one exact definition for "sport." Wikipedia and World Book's definitions don't say that physical activity is a must, whereas dictionary.com's does require it.
I wonder how many calories a grandmaster burns during an important match... I bet it's a heck of a lot more than what you'd burn watching the game, although to outward appearances, the level of physical effort would look about the same. I think that those who consider chess a sport (and officially speaking, we're talking dozens of nations) are simply open to a broader definition of 'exertion' than the nay-sayers.
And to argue that this exertion is something other than physical is tantamount to saying that the brain is somehow a thing apart from the rest of the body - like it runs on magic or something.