Before the modern era, the game was only well-known in China, Korea and Japan, but it was ultimately the Japanese that played a large role in spreading the game outside of east Asia, with most of the cultural exchange occurring as recently as the 19th and 20th centuries. So, across a lot of the world, in many different languages, the name for the game is the loanword “Go” in homage to Japan’s part in proliferating the game.
While the Chinese definitely deserve credit for inventing the game, I think many of us might not even be here talking about the game, if not for the Japanese.
The evolution of the rules is another interesting part of Go history, which I discussed a bit in another post: Pondering Upon The Rules Of Go - #17 by yebellz
The summary of that is that both the modern Japanese and Chinese rules are descended from a common ancestor (stone scoring), rather than the former being descended from the latter. It was this ancient form of the rules that was likely spread from China into Japan and Korea.