stickball game vs baseball

stickball game and baseball both are nouns.

Word	Noun	Adjective	Verb	Adverb
stickball game	Yes	No	No	No
baseball	Yes	No	No	No

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

stickball game: a form of baseball played in the streets with a rubber ball and broomstick handle
baseball: 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 stickball game include ball, baseball game.

stickball game (noun)	baseball (noun)
a form of baseball played in the streets with a rubber ball and broomstick handle	a ball game played with a bat and ball between two teams of nine players; teams take turns at bat trying to score runs
	a ball used in playing baseball