athletic game vs athletics

athletic game and athletics both are nouns.

Word	Noun	Adjective	Verb	Adverb
athletic game	Yes	No	No	No
athletics	Yes	No	No	No

As nouns, athletics is a hypernym of athletic game; that is, athletics is a word with a broader meaning than athletic game:

Other hypernyms of athletic game include game, sport.

athletic game (noun)	athletics (noun)
a game involving athletic activity	an active diversion requiring physical exertion and competition
	participation in sports events as an extracurricular activity
	a contest between athletes