From Dictionary.com:
"sport
[spawrt, spohrt] Show IPA
noun
1.
an athletic activity requiring skill or physical prowess and often of a competitive nature, as racing, baseball, tennis, golf, bowling, wrestling, boxing, hunting, fishing, etc. "
"game
1 [geym] Show IPA noun, adjective, gam·er, gam·est, verb, gamed, gam·ing.
noun
1.
an amusement or pastime: children's games. "