WordWeb Pro gives its own set of meanings, and summarises those from Chambers and the OED as follows:-
WordWeb Pro
1. An active diversion requiring physical exertion and competition
2. The occupation of athletes who compete for pay
3. (Maine colloquial) a temporary summer resident of Maine
4. A person known for the way she (or he) behaves when teased, defeated or subjected to trying circumstances
5. Someone who engages in sports
6. (biology) an organism that has characteristics resulting from chromosomal alteration
7. Verbal wit or mockery (often at another's expense but not to be taken seriously)
Chambers
1. Recreation
2. A pastime
3. Play
4. A game or activity, esp one involving physical exercise
5. A specific, esp outdoor, amusement, activity or recreation
6. Success in or pleasure from shooting, fishing, or the like
7. Amusement, fun, good-humoured mirth
8. Mockery, contemptuous mirth
9. An object of mockery, a laughing stock
10. A plaything (esp figurative)
11. Dalliance, amorous behaviour
12. A person of sportsmanlike character, a good fellow
13. A form of address, used esp between males (Aust and NZ)
14. An animal or plant that varies singularly and spontaneously from the normal type
OED
1. An activity involving physical exertion and skill in which an individual or team competes against another or others for entertainment:
2. (sports) Brit. an occasion on which people compete in various athletic activities:
3. [mass noun] [usu. with adj.] success or pleasure derived from an activity such as hunting or fishing
4. [mass noun] dated entertainment; fun:
5. archaic a source of amusement or entertainment:
I think we can conclude that there is no one universally accepted meaning. For things like the Olympic Games (note: not Olympic Sports) it seems to be necessary to call yourself a sport so that you can attract funding. Hence such creations as Dance Sport.