The problem is that sport and game cross over in many places from big team sports like cricket/baseball/football/soccer to small team sport like volleyball/pairs tennis to individual sports like singles tennis/bowling, all of which are also games. Then there are some things that are clearly games that require physical skills that many argue are also sports like billiards. But poker is just a game. Big tournaments are also endurance based, but it's mental endurance versus physical as there is a lot of mental stress and being alert is key to making a deep run.
To me, if it requires physical skill, it's sport. If it requires mental, it is game. If it is some of both, then it is both. Track and field is just sport as the best physical specimen wins. Baseball is both as the pitcher and the catcher play a mental game with the batter on every pitch just as football pits strategy against strategy. Soccer, now, is more sport than anything. There is a certain awareness required, but not being a regular fan, I don't know if there is enough mental aspect to it to call it a game. And I feel much the same with bowling and golf. You just go out and do your best score each frame or hole. The mental aspects are only about how to pick up a spare or how to get out of a sandtrap.
But it is a very fine line making those decisions between being sport, game, or both.