stickball game vs stickball

stickball game and stickball both are nouns.

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

As nouns, stickball game and stickball are synonyms defined as:

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

stickball game (noun)	stickball (noun)
a form of baseball played in the streets with a rubber ball and broomstick handle	a form of baseball played in the streets with a rubber ball and broomstick handle