Not all of them really look the same, the Eastern Asian races have different phenotypes just like other continent's races do. So some of that just comes down to a matter of perspective. There is also the lack of popularity of certain, clothing styles, hairstyles, or body modifications such as tattoos in certain places in East Asia (try to find an East Asian with a mullet) so that also contributes to similar looks.
However, way back in history, there were great conquerors such as Genghis Khan, who killed off great numbers of the East Asian population and then subsequently seeded a lot of the remaining women. Thus spreading the same genetics around, which is why you always see people talking about how thousands of people today have Genghis Khan as an ancestor. And it was also common for the nobility in areas like this to have many offspring that branched out into huge families, while some peasantry family bloodlines stayed small or died off.