pinball vs pinball game

pinball and pinball game both are nouns.

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

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

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

pinball (noun)	pinball game (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