好棋 means "a good move"; either in chess-style games or, by analogy, anything related to a contest of strategy (e.g.
普京毁了一步好棋, "Putin screwed up a (previous) good move".)
The phrase in question,
中国好棋, is a bit different. That originated from this poster,
where it is the title of a poem:
好 has two meanings:
- adjective "good"
- verb "to like"
The latter meaning is the one intended in the phrase ``. So the phrase is saying "China likes chess" (or Go or generic board games). This can be inferred from the context provided by the poem, the visual emphasis on the
好 character, and also because a subject (
中国) precedes it and an object
棋 follows it.
The other possible meaning for the phrase is something along the lines of a "Chinese good move". That doesn't fit the poster's context (though you can interpret it as a pun), but the phrase can be used with that meaning too.
For instance, Chinese chess prodigy 侯逸凡 (Hou Yifan) has talked about the awakening Chinese dragon making a
中国好棋 on the chessboard of the world.
For reference, the poster: