lottery vs gambling game

lottery and gambling game both are nouns.

Word	Noun	Adjective	Verb	Adverb
lottery	Yes	No	No	No
gambling game	Yes	No	No	No

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

lottery: players buy (or are given) chances and prizes are distributed by casting lots
gambling game: a game that involves gambling

Other hypernyms of lottery include game of chance.

lottery (noun)	gambling game (noun)
players buy (or are given) chances and prizes are distributed by casting lots	a game that involves gambling
something that is regarded as a chance event