Basically it seems that sport is any competition where the game must rely on a certain amount of physical dexterity, even if logical dexterity also happens to come in to it.
Chess won't tend to get counted as a sport because the physical aspect (of picking up the pieces) isn't unique enough to the competitor (they could even ask somebody else, or a robot, to pick up the pieces for them). So even though the logical aspect of the game would seem to place it far above many sports in that respect, it still makes snooker a sport, with the Olympic ideals and all that entails, and chess a game with Ludo and Snakes and Ladders and all that entails.
Playing a videogame is actually often a sport in a way. The physical aspect is often unique to the player (it's not like there is often time to give instructions to someone else to do the movements on screen). So the fact that chess is always turn based will seemingly never make it a sport and yet the fact that videogames are often real time could make it a sport.
By that definition, darts is a sport (it's like a working class archery I suppose) because it does rely on a certain amount of physical dexterity, even if that is just carefully executing a trajectory as an ice skater might.
But so is throwing a hoop over a rubber duck at a fair.
I have sympathy with those who say that ice skating shouldn't be a sport because it depends on the opinion on the judges. But it doesn't really bother me too much because I think that they are all, in essence, just games albeit ones that can carry a certain weight to them due to the regimented dedication and sometimes strength of their players. And that can be personal to the player. Others do it because it's a bit of a laugh, a time filler, a way of meeting people.