Most of the "Western" civilizations old enough to attempt comparison with China were not European in the modern sense at all. The classic example is usually Rome, which treated most of Europe as barbarians to colonize and enslave. The engine and wealth of the empire was along the Mediterranean. Ancient Rome was thus really a Mediterranean power not a "European" one. I think you could successfully argue Romans had more in common with other ancient Mediterranean powers or even ancient Mesopotamians than modern Europeans.
As to the rest of your points true enough. It is well known that today's Europeans find themselves in between a rock and a hard place given the current split between American and Chinese hegemony.
The Roman Empire covered much of Europe about 2000 years ago, and those places have had a great deal of cultural continuity since then.
It does not map to modern Europe. It encircles the Mediterranean with much of Europe either not included or on the periphery. Most of Europe was to the Romans barbarian hinterland 2000 years ago. Even at its greatest extent you will see Rome was always centered on the Mediterranean. The "West" would have been entirely alienated from said culture had the flame not been kept alive by the East when the West fell.