ice hockey vs athletic game

ice hockey and athletic game both are nouns.

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

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

ice 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
athletic game: a game involving athletic activity

Other hypernyms of ice hockey include contact sport.

ice hockey (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