passing game vs passing play

passing game and passing play both are nouns.

Word	Noun	Adjective	Verb	Adverb
passing game	Yes	No	No	No
passing play	Yes	No	No	No

As nouns, passing game and passing play are synonyms defined as:

passing game and passing play: (American football) a play that involves one player throwing the ball to a teammate

Other synonyms of passing game include pass, passing.

passing game (noun)	passing play (noun)
(American football) a play that involves one player throwing the ball to a teammate	(American football) a play that involves one player throwing the ball to a teammate