game room vs recreation room

game room and recreation room both are nouns.

Word	Noun	Adjective	Verb	Adverb
game room	Yes	No	No	No
recreation room	Yes	No	No	No

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

game room: a recreation room for noisy activities (parties or children's play etc)
recreation room: a room equipped for informal entertaining

Other hypernyms of game room include rec room.

game room (noun)	recreation room (noun)
a recreation room for noisy activities (parties or children's play etc)	a room equipped for informal entertaining