So, I was interested in this particular boardgame called Xiangqi. It’s a Chinese version of Chess. But it’s hard to search sources for this game in English. It’s hard for non-chinese to knows more about Chinese culture because the lack of English sources.
As others have said, China is interested in mutual development, not US style hegemony of which the high cultural influence is a part. I would also add that spreading a language is part of cultural influence, and this may occur regardless of China’s geopolitical stance because as they become increasingly important people will learn Mandarin to work and study with them, and in the process getting access to and being exposed to Chinese culture. You can see some cultural export with the Confucius Institutes which the US for the most part forced universities to close down, but notice that these are also about teaching Mandarin.