running game vs football play

running game and football play both are nouns.

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

As nouns, football play is a hypernym of running game; that is, football play is a word with a broader meaning than running game:

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

running game (noun)	football 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 by the offensive team