It's quite simple, actually. I came up with a classification system years ago, and I'll post a simplified version here. Board games and card games do not figure into this system of classification at all, because they are in no way athletic. For purposes of this classification system, you must have some kind of physical manipulation of your body that influences the game. No..bluffing in poker does not count. Now, let's move on.
There are four types of events: sports, games, competitions, and races. A sport requires an opponent that will actively attempt to deter you...a defense, if you will. Baseball, football (american version and otherwise), basketball, tennis, etc...
Bowling and golf are not sports, they are games. Games are anything that you can do pretty much on your own and get the same result as if you were "playing against" someone. Darts is another example.
Competitions are any game where judging comes into play. Boxing is still a sport because it involves a defense, unlike a game, and because the judges are not the only way of determining a winner. Cheerleading, gymnastics, and ice skating, however, are all competitions. (Fun fact, this entire classification system came about because some girl my freshman year of college wanted to convince me that cheerleading was a sport.)
Finally, we come to races, which should be obvious by the name. Anything that measures who gets something accomplished first. Swimming, running, and cup stacking come to mind.
There you have it! In the unlikely chance anyone wants to use this somewhere else, please, at least, credit me. It's saved me tons of arguments since I developed it. ;)