I prove you wrong, cause following your idea, studying mathematics would be a sport..
chess is a game, relax lol
First, sports are games too. Secondly, mathematics are not directly competitive like chess. For example, if I do better on a test, it doesn't mean that the rest of the class is getting an F. Anyway, don't tell me chess isn't a sport when my heart is beating faster in the heat of a tough OTB game than it does when I'm running a mile.
Probably, the most accurate categorization is: mind sport. Although, to play good chess competitively, it helps immensely to be fit. The mind-body connection is important.
Chess is not a sport, it is something much greater than a mere sport.