Dairy products have not, historically, been a part of the Chinese or Japanese diet. Since food traditions run deep in both of these cultures, there is little presence of dairy in local foods. Of course, there are Starbucks and cheeseburger joints all over.
However, the dairy industry developed rapidly in Japan after WWII (starting in Hokkaido), and is now a major presence nationwide. You will find many milk products, yogurt, and some cheeses in every shop in Japan. Increasingly, diary is finding its way onto Japanese tables. In fact, Japanese people drink milk as a beverage much more than Americans do.
In China, the dairy industry began to explode around 10 years ago. Chinese officials observed how the Japanese are now taller, on average, than Chinese and attributed some of this to milk consumption. State support for dairy farming and dairy companies has been significant, and dairies are now found all over the country (not just in the traditional dairy region of Mongolia).
Western corporate influence is also a big factor.