My question is specifically referring to the fact that in many longest lasting empire lists, the Roman Empire is said to have lasted from 27 BC to 1453 AD. But why are the different dynasties of Rome considered a single empire but not, let's say, the Chinese Dynasties.

One common response I see is that the culture, administration, offices, etc were preserved throughout the reigns of the different dynasties of Rome. Were none of the Confucian analogues preserved similarly in China? And what about the dynasties that ruled Magadha from Pataliputra? By the same yardstick, shouldn't the Haryanka, Shishunaga, Nanda, Maurya and Shunga dynasties be considered one empire?

How is the Three Kingdoms Period different from something like the Crisis of the Third Century or the period of the rump states following the sack of Constantinople?

The seat of power changed in the case of the Roman Empire too. In fact, for much of its history, Rome was no longer part of the Empire. And if we consider ethnicities, yes, the Jurchens and Mongols ruled China but many of the ruling emperors and dynasties of Rome were not ethnic Latins. Especially all the successive Greek Dynasties in the East.

Thanks!