hockey game vs athletic game

hockey game and athletic game both are nouns.

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

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

hockey game: 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
athletic game: a game involving athletic activity

Other hypernyms of hockey game include contact sport.

hockey game (noun)	athletic game (noun)
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	a game involving athletic activity