There have been plenty of rises and falls of civilization in China in the intervening thousands of years. It's way reductionist to claim that this is all the same one unflagging continuous empire.

In a way, you're doing Chinese history a huge disservice by making it a lot less interesting than it actually is when you claim that it's all just one empire persisting steadily through time.

And anyway, "the west" has a continuous history going all the way back through the ancient Greeks. That's at least two and a half millennia. It's not been the same people or the same empire since then, obviously (same for China), but the continuous written history easily goes back at least that far.