pinball game vs pinball

pinball game and pinball both are nouns.

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

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

pinball game and pinball: a game played on a sloping board; the object is to propel marbles against pins or into pockets

pinball game (noun)	pinball (noun)
a game played on a sloping board; the object is to propel marbles against pins or into pockets	a game played on a sloping board; the object is to propel marbles against pins or into pockets