chess vs chess game

chess and chess game both are nouns.

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

As nouns, chess and chess game are synonyms defined as:

chess and 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

chess (noun)	chess 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 board game for two players who move their 16 pieces according to specific rules; the object is to checkmate the opponent's king
weedy annual native to Europe but widely distributed as a weed especially in wheat