golf game vs match play

golf game and match play both are nouns.

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

As nouns, match play is a hyponym of golf game; that is, match play is a word with a more specific, narrower meaning than golf game:

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
match play: golf scoring by holes won

golf game (noun)	match play (noun)
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	golf scoring by holes won