twenty-one vs card game

twenty-one and card game both are nouns.

Word	Noun	Adjective	Verb	Adverb
twenty-one	Yes	Yes	No	No
card game	Yes	No	No	No

As nouns, card game is a hypernym of twenty-one; that is, card game is a word with a broader meaning than twenty-one:

twenty-one: a gambling game using cards; the object is to hold cards having a higher count than those dealt to the banker up to but not exceeding 21
card game: a game played with playing cards

Other hypernyms of twenty-one include cards.

twenty-one (noun)	card game (noun)
a gambling game using cards; the object is to hold cards having a higher count than those dealt to the banker up to but not exceeding 21	a game played with playing cards
the cardinal number that is the sum of twenty and one

twenty-one (adjective)	card game (adjective)
being one more than twenty