game of chance vs gambling

game of chance and gambling both are nouns.

Word	Noun	Adjective	Verb	Adverb
game of chance	Yes	No	No	No
gambling	Yes	Yes	No	No

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

game of chance: a game that involves gambling
gambling: the act of playing for stakes in the hope of winning (including the payment of a price for a chance to win a prize)

Other hypernyms of game of chance include gaming, play, game.

game of chance (noun)	gambling (noun)
a game that involves gambling	the act of playing for stakes in the hope of winning (including the payment of a price for a chance to win a prize)

game of chance (adjective)	gambling (adjective)
	preoccupied with the pursuit of pleasure and especially games of chance