"Sport is all forms of physical activity which, through casual or organised participation, aim to use, maintain or improve physical fitness and provide entertainment to participants" - from Wikipedia
Sport is associated with physical activity, which chess is not and therefore i do not consider it as sport.
If you say the mental/pyschological aspect makes it a sport, you also agree that E-"sports" like Counterstrike, Warcraf or Starcraft is sport aswell.
And that is something i do not see.