It's not necessarily unique, however. While European civilisation is more fragmented by nationalism, by comparison there's clear lineage through religion, law, culture, etc. Much like China's lineage was really kick-started by the Han, Europe still owes much to Rome. If you get right down to detail then sure, there's a difference in the character of the cultural journey, but I think the principle is similar.
I agree. China is more isolated geographically and hence less diverse than Europe and hence it is still quite different. It is definitely not the only culture that passed that long though.