blindman's buff vs child's game

blindman's buff and child's game both are nouns.

Word	Noun	Adjective	Verb	Adverb
blindman's buff	Yes	No	No	No
child's game	Yes	No	No	No

As nouns, child's game is a hypernym of blindman's buff; that is, child's game is a word with a broader meaning than blindman's buff:

blindman's buff: a children's game in which a blindfolded player tries to catch and identify other players
child's game: a game enjoyed by children

blindman's buff (noun)	child's game (noun)
a children's game in which a blindfolded player tries to catch and identify other players	a game enjoyed by children