Definitions of sport:
1) Physical activity that is governed by a set of rules or customs and often engaged in competitively.
2) A particular form of this activity.
3) An activity involving physical exertion and skill that is governed by a set of rules or customs and often undertaken competitively.
4) An active pastime; recreation.
Definitiond of game:
1) An activity providing entertainment or amusement; a pastime: party games; word games.
2) a) A competitive activity or sport in which players contend with each other according to a set of rules: the game of basketball; the game of gin rummy.
b) A single instance of such an activity: We lost the first game.
c) GAMES: An organized athletic program or contest: track-and-field games; took part in the winter games. [like the Olympics]
d) A period of competition or challenge: It was too late in the game to change the schedule of the project.
3) a) The total number of points required to win a game: One hundred points is game in bridge.
b) The score accumulated at any given time in a game: The game is now 14 to 12.
4) The equipment needed for playing certain games: packed the children's games in the car.
5) A particular style or manner of playing a game: improved my tennis game with practice.
Definitions of art:
1. the quality, production, expression, or realm, according to aesthetic principles, of what is beautiful, appealing, or of more than ordinary significance.
2. the class of objects subject to aesthetic criteria; works of art collectively, as paintings, sculptures, or drawings: a museum of art; an art collection.
3. a field, genre, or category of art: Dance is an art.
4. the fine arts collectively, often excluding architecture: art and architecture.
5. any field using the skills or techniques of art: advertising art; industrial art.
6. (in printed matter) illustrative or decorative material: Is there any art with the copy for this story?
7. the principles or methods governing any craft or branch of learning: the art of baking; the art of selling.
8. the craft or trade using these principles or methods.
9. skill in conducting any human activity: a master at the art of conversation.
10. a branch of learning or university study, esp. one of the fine arts or the humanities, as music, philosophy, or literature.
11. arts, a. (used with a singular verb) the humanities: a college of arts and sciences.
b. (used with a plural verb) liberal arts.
12. skilled workmanship, execution, or agency, as distinguished from nature.
13. trickery; cunning: glib and devious art.
14. studied action; artificiality in behavior.
15. an artifice or artful device: the innumerable arts and wiles of politics.
16. Archaic. science, learning, or scholarship.
And a definition of hobby:
1. an activity or interest pursued for pleasure or relaxation and not as a main occupation: Her hobbies include stamp-collecting and woodcarving.