stroke play vs golf game

stroke play and golf game both are nouns.

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

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

stroke play: golf scoring by total strokes taken
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 stroke play include golf.

stroke play (noun)	golf game (noun)
golf scoring by total strokes taken	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