chess game vs board game

chess game and board game both are nouns.

Word	Noun	Adjective	Verb	Adverb
chess game	Yes	No	No	No
board game	Yes	No	No	No

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

chess game: a board game for two players who move their 16 pieces according to specific rules; the object is to checkmate the opponent's king
board game: a game played on a specially designed board

chess game (noun)	board game (noun)
a board game for two players who move their 16 pieces according to specific rules; the object is to checkmate the opponent's king	a game played on a specially designed board