GAME - A competitive one played according to the rules and decided by skill, strength, or luck.
SPORT – a game or competitive activity especially an outdoor one involving physical exertion. Eg cricket, football, racing and hunting
Therefore a sport is a game played in accordance to the rules of play
We all play a game of Tennis; a round of Golf; a game of Squash; Shooting is always known as Shooting (but still a sport)
I think if an individual does it, such as running, swimming etc, they compete against the clock it’s referred to as a sport, But collectively running swimming etc can be classified as games such as in the Olympics
But is Ballroom dancing a sport
The sport of Kings – but they only bet on the outcome, but not race them selves.