a song of ice and fire - Do Oriental-style civilisations exist in A Game of Thrones?

I haven't read the books; I've only watched the TV series.

Are there any civilisations in A Game of Thrones similar in appearance to Japanese or Chinese cultures (race, buildings, clothes and others cultural aspects)?

The show features a few sets of non-Caucasians:

Dornishmen tend to have olive skin and dark hair, with blondes being rare in that region. Their accents on the TV show seem to suggest a Middle Eastern or Mediterranean culture.

We have also seen the Magnar of Thenn and his people being portrayed as a Slavic or Russian folk.

Answer

I am not exactly sure what you are looking for but the closest civilization shown so far may be the Dothraki, who according to GRRM:

The Dothraki were actually fashioned as an amalgam of a number of steppe and plains cultures... Mongols and Huns, certainly, but also Alans, Sioux, Cheyenne, and various other Amerindian tribes... seasoned with a dash of pure fantasy. So any resemblance to Arabs or Turks is coincidental. Well, except to the extent that the Turks were also originally horsemen of the steppes, not unlike the Alans, Huns, and the rest.

But he goes on to say:

There do exist many other cultures and civilizations in my world, to be sure. The peoples of Yi Ti have been mentioned, as have the Jogos Nhai. I am not sure to what extent those peoples will ever enter this present story, however... their lands are very far away.

[...]

In general, though, while I do draw inspiration from history, I try to avoid direct one-for-one transplants, whether of individuals or of entire cultures. Just as it not correct to say that Robert was Henry VIII or Edward IV, it would not be correct to say that the Dothraki are Mongols.