penny ante poker vs poker game

penny ante poker and poker game both are nouns.

Word	Noun	Adjective	Verb	Adverb
penny ante poker	Yes	No	No	No
poker game	Yes	No	No	No

As nouns, poker game is a hypernym of penny ante poker; that is, poker game is a word with a broader meaning than penny ante poker:

penny ante poker: poker played for small stakes
poker game: any of various card games in which players bet that they hold the highest-ranking hand

Other hypernyms of penny ante poker include poker.

penny ante poker (noun)	poker game (noun)
poker played for small stakes	any of various card games in which players bet that they hold the highest-ranking hand