rushing vs running game

rushing and running game both are nouns.

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

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

rushing: (American football) an attempt to advance the ball by running into the line
running game: (American football) a play in which a player attempts to carry the ball through or past the opposing team

Other hypernyms of rushing include run, running, running play.

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