running play vs running game

running play and running game both are nouns.

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

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

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

Other synonyms of running play include run, running.

running play (noun)	running game (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