It's a definitional difference. The history of sports is much more martial than games, though, some games are applicable to developing martial prowess. 

Look at the sports in the original Olympics. People died in those. 

Playing a game is not the same thing as competing in a sport. 

This is no commentary on athleticism by those who play professionally or compete professionally. 

Another way to look at it is the sports are things you do: you swim, you wrestle, you throw a javelin. There usually are only one or two rules and possibly a safety consideration or two because we're all too civilized these days. 

For that matter, bowling and curling are sports, where as all other ball games that I'm aware of are just that: games you play. 

The fanaticism is gross. Too many people live vicariously through "their team." too many men, especially, neglect responsibilities for those kinds of vicarious thrills. I find that a very menial mentality. 🤷‍♂️