Anything that is competitive and has objective criteria in order to score points/win. Skipping has no competitive element, so I'd classify it as a physical activity rather than a sport. Chess and poker are competitive and highly skilled, but with no physical activity, so I'd probably classify them as mind sports. The ones I have an issue with are things like figure skating and synchronised swimming. The skill level is incredible, but anything that relies on the subjective opinion of a judge for scoring, even ones operating within a defined framework, as deeply flawed as a competitive sport in my opinion. Having said that, I'm looking forward to taking in a bit of dressage at the Olympics. Because who doesn't love disco dancing horses?
I'm not a big boxing fan, but I often hear people questioning one or more of the judges' decisions at the end of a bout.
Here you go. Encyclopedia Britannica. Games and sports are very similar: a game is a physical or mental activity or contest that has rules and that people do for pleasure. A sport is a contest or game in which people do certain physical activities according to a specific set of rules and compete against each other. The difference is subtle. A game is any mental or physical activity with rules that is done for fun, such as physical activities like baseball and soccer, or board games such as chess and Monopoly, or card games, or electronic games (like apps), or video games. Sports are specific physical activities one can compete in such as baseball, soccer, football, field hockey, running, cycling, rock climbing, swimming, diving, race car driving, kayaking, or weight lifting. So as you can see some fit into both categories.
Hunting, and to an extent, fishing aren't sports. A sport is when your opponent has a fighting chance to win.
If you explained dressage to me and I had never heard of it, I would laugh and say must be terrible to watch. But every Olympics I'm mesmerised by it!!
I think the best definition, (if a little abstract) that I've heard is that a sport is one where you need to change your shoes.