Thank you for participating in this conversation with me, Kouen.
I will concede that your argument is sound and based in our current language. English is an ever-evolving language that borrows from many languages. Some of the languages we borrow from have borrowed from others in turn.
I can not argue that your logic is faulty. With the current definition of sport, chess does fit within its confines, and is also recognized by associations. This is not a concession.
The fault with the word sport is that it is too loosely defined. If you trace the word sport to its Latin origin, you will find that the Latin origin word is "portare," which means "to carry." Portare becomes the French "desporter" which means "to carry away," though this can be taken metaphorically as in to carry one's troubles away with entertainment. Desporter becomes the Old English "sporten" which means to "take pleasure, enjoy, or amuse oneself". I argue that the root of this word "portare" seems to allude to physical competition, even if our current definition disagrees.
Competitions such as chess, poker, backgammon, mancala, even Pokemon, Yu-Gi-Oh, and other games alike them, all deserve their own categorical term. There are many other games that would fit in this category. The definition of a game that would fit in this category is "any competition that does not have to have physical intervention to be played", as in the only determining factor of the outcome of the competition will come directly from understanding of the game, and that physical skill is not necessary, only intellectual understanding.
Many competitions, no matter how good you are at understanding the rules and possible ways to win, physicality is a factor of winning or losing. Considering the Latin portare, I believe that sports should be the competitions that necessary need physical intervention.
Chess can be played by anyone regardless of shape, size, gender, or physical ability. The only factor that matters in the game or chess is ones understanding of how to play. Video games are one competition that seems to fit here but do not, as they necessitate a need of physical intervention, albeit small, it still requires a player to have hands.
The term I propose for this new category of competition is "cogni". This word follows a similar etymological pathway as "sport". From Latin, through French, to English. The Latin "cognocere" means "to get to know, to recognize." The French term "conoistre" means "to know." There's a bit more in the etymological timeline, but I believe the point is made.
https://www.etymonline.com/word/cognizance
Cogni is a term that refers to any competition that can be had without any sort of physical intervention necessary by the one actually competing. For example, Stephen Hawking or a similarly disabled person could play chess without ever having to touch the Chess board. Someone may have to move the piece, or have it displayed on a screen, but the actual input that matters is the intellectual input only. For this reason, competitive speed Rubik's solving is within the confines of a sport, while chess, poker, and any other game that only requires cognitive input should be given their own terms as to not be lumped in so carelessly with other forms of competition.
I believe that the fact we have the urge to have the discussion of whether or not chess is a sport is a qualifying factor as to why it should have its own distinguished classification that will separate games of the mind from games of the body.
For instance, imagine a device that reads simple input to the game by brainwaves. Turn based, competitive games that measure intellect, not reaction time, speed, or physical skil should have their own classification, as I believe is demonstrated by the very fact this conversation is being had.