My simplistic opinion: to be a sport, the winner must achieve a specific, measurable goal that results in a final decisive outcome. A sport also requires at least a moderate amount of athleticism to perform.
Examples: Baseball, Basketball, Football, Hockey and similar things all have a specific goal that the winner is the team/person that scores the most points (or least in golf) by a specific point system. Skiing/Racing/Swimming also fits in as sports since a winner is the one with the best times.
Boxing fits as a sport because the goal is to make the competitor unable to perform via a knockout or TKO. granted they don't all end that way but most of the ones that require judging are pretty definitive who made the most connections on punches and registered the most damage.
Figure skating, Snowboard halfpipes, aerial skiing and other activities like those that require someone's opinion to determine a winner aren't what I would consider sports. I'd consider them contests or competitions.
Darts, curling, golf and bowling too for that matter I would consider games. There's competition but not much athleticism.