running game vs running play

running game and running play both are nouns.

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

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

running game and running play: (American football) a play in which a player attempts to carry the ball through or past the opposing team

Other synonyms of running game include run, running.

running game (noun)	running play (noun)
(American football) a play in which a player attempts to carry the ball through or past the opposing team	(American football) a play in which a player attempts to carry the ball through or past the opposing team