I would say that Chinese influence is not lost, much less Ancient particles, but they become more diluted, mixed, or otherwise evolved to become what we would consider Japanese, Korean, or SEA cultures. Keep in mind that culture and traditions are not static, but very much alive and breathing, and like all things living, they change over time if they are to survive into the modern day.
Much of today's practices of respect for your elders, and the overly flowery words and phases that Chinese culture are known for, all stern from eons ago, by a guy called Confucius, and the importance of literature and education of Han China unto the population, as that is how the select for a government official, thus, everyone was thrive for it.
As for why the Western world seldom comes into contact with Chinese culture, it all comes down to the political climate right now. See that Japan and S. Korea are two of the largest political allies of the US, NATO, and thus the Western world AGAINST China, it is not hard to see why there is an explosion in popularity of one, and the lack of the other. If you are in SEA, such as Lao, Vietnam, or the region around them, then the Chinese culture, or the influences of Chinese cultures is everywhere.