athletic game vs hockey

athletic game and hockey both are nouns.

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

As nouns, hockey is a hyponym of athletic game; that is, hockey is a word with a more specific, narrower meaning than athletic game:

athletic game: a game involving athletic activity
hockey: a game played on an ice rink by two opposing teams of six skaters each who try to knock a flat round puck into the opponents' goal with angled hockey sticks

Other hyponyms of athletic game include hockey game, ice hockey, tetherball, water polo, outdoor game, court game.

athletic game (noun)	hockey (noun)
a game involving athletic activity	a game resembling ice hockey that is played on an open field; two opposing teams use curved hockey sticks try to drive a ball into the opponents' net
	a game played on an ice rink by two opposing teams of six skaters each who try to knock a flat round puck into the opponents' goal with angled hockey sticks