I don’t like sqweels’ definition, since it technically includes, say, gang fights, warfare, or just ordinary dancing.
The operating definition we used in my sport class was that a sport is a contest of physical skill with defined criteria for determining a winner, played for its own purpose.
Archery, by that definition, is a sport (and to be honest I am amazed anyone would say it wasn’t.)
Ballroom dancing, figure skating et al. are sort of on the bubble. While they are mostly contests of physical skill, they are to greater or lesser degrees also contests of artistic agreement and fashion. It’s difficult to make the argument that something is completely a sport when the winner is determined to some extent by things that have nothing to do with physical skill. The SUBJECTIVITY really doesn’t bother me - I mean, football, baseball and basketball all have degrees of subjectivity in the official’s interpretation and calling of the rules. However, in those cases the officials are making decisions on objective outcomes of physical skill - was the ball a strike or not, did the reciever get both his feet down inbounds.
Officials in figure skating assign half the score based on something that is not a matter of athletic prowess. So I think clearly there is a sliding scale in some respects. Gymnastics, which is subjectively judged but really has no artistic aspect to it at all, is 99.9% a sport; singles figure skating, which is clearly mostly athletic but has a large artistic element, is maybe only 60% a sport.
To my mind, the percieved “difficulty” os a sport is irrelevant. Billiards to my mind is very obviously a sport and I cannot think of any rational or logical reason why it is not. Maybe you don’t sweat a lot doing it or have to be strong, but it’s sure as hell a sport, and if you don’t believe me, ask a decathlete to go 1-on-1 with a top ranked shark over a game of 9-ball and see if he lasts ninety seconds.