stickball vs stickball game

stickball and stickball game both are nouns.

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

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

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

stickball (noun)	stickball game (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