go game vs board game

go game and board game both are nouns.

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

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

go game: a board game for two players who place counters on a grid; the object is to surround and so capture the opponent's counters
board game: a game played on a specially designed board

go game (noun)	board game (noun)
a board game for two players who place counters on a grid; the object is to surround and so capture the opponent's counters	a game played on a specially designed board