running game vs rushing

running game and rushing both are nouns.

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

As nouns, rushing is a hyponym of running game; that is, rushing is a word with a more specific, narrower 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
rushing: (American football) an attempt to advance the ball by running into the line

Other hyponyms of running game include draw, draw play, end run, sweep, return, reverse, rush.

running game (noun)	rushing (noun)
(American football) a play in which a player attempts to carry the ball through or past the opposing team	(American football) an attempt to advance the ball by running into the line
	the act of moving hurriedly and in a careless manner