no-hit game vs baseball game

no-hit game and baseball game both are nouns.

Word	Noun	Adjective	Verb	Adverb
no-hit game	Yes	No	No	No
baseball game	Yes	No	No	No

As nouns, baseball game is a hypernym of no-hit game; that is, baseball game is a word with a broader meaning than no-hit game:

no-hit game: a game in which a pitcher allows the opposing team no hits
baseball game: a ball game played with a bat and ball between two teams of nine players; teams take turns at bat trying to score runs

Other hypernyms of no-hit game include ball, baseball.

no-hit game (noun)	baseball game (noun)
a game in which a pitcher allows the opposing team no hits	a ball game played with a bat and ball between two teams of nine players; teams take turns at bat trying to score runs