stickball vs baseball game

stickball and baseball game both are nouns.

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

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

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

stickball (noun)	baseball game (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