match play vs golf game

match play and golf game both are nouns.

Word	Noun	Adjective	Verb	Adverb
match play	Yes	No	No	No
golf game	Yes	No	No	No

As nouns, golf game is a hypernym of match play; that is, golf game is a word with a broader meaning than match play:

match play: golf scoring by holes won
golf game: a game played on a large open course with 9 or 18 holes; the object is use as few strokes as possible in playing all the holes

Other hypernyms of match play include golf.

match play (noun)	golf game (noun)
golf scoring by holes won	a game played on a large open course with 9 or 18 holes; the object is use as few strokes as possible in playing all the holes