According to Wikipedia, sport is defined as follows
Sport (or sports) is all forms of usually competitive physical activity which, through casual or organised participation, aim to use, maintain or improve physical ability and skills while providing entertainment to participants, and in some cases, spectators. Hundreds of sports exist, from those requiring only two participants, through to those with hundreds of simultaneous participants, either in teams or competing as individuals.
According to Google definition
Sport is an activity involving physical exertion and skill in which an individual or team competes against another or others for entertainment.
Thus, it seems to boil down to whether chess is a physical activity and skill. To begin with, as far as I know, the majority of the world's population does not regard chess as a sport but rather as a board game. Yet, when focusing on the skill set required to be great at chess, the physical factors are significant. Perhaps not as much the actual motion of moving the pieces and pressing the chess clock. Although there is a certain skill in executing your moves quickly and flawlessly. Yet more in terms of physical endurance. The ability to stay focused and sharp for a long period of time (e.g. 6 hours). The ability to make 40 or more good decisions during that time span. The mind set to win the game. There is also an undeniable amount of entertainment in top level chess!
My answer is that chess can be defined as a sport. But it is not considered to be a sport, because it is a board game, and board games are not associated to sports.