backgammon board vs gameboard

backgammon board and gameboard both are nouns.

Word	Noun	Adjective	Verb	Adverb
backgammon board	Yes	No	No	No
gameboard	Yes	No	No	No

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

backgammon board: the board on which backgammon is played
gameboard: a flat portable surface (usually rectangular) designed for board games

Other hypernyms of backgammon board include board.

backgammon board (noun)	gameboard (noun)
the board on which backgammon is played	a flat portable surface (usually rectangular) designed for board games