The “West” is in a cultural, not a past geographic context
Right. The culture of "the West" can be traced back to Jerusalem, which gave us the idea that life is journey, with a beginning and an end, not endless cycles of one damned thing after another; through Athens, which gave us the idea that human reason is capable of getting at the truth of things; through Rome, that gave us the idea that law was better than brute force; through the Medieval philosophers who gave us the idea that the universe is a rational place because it was created by a rational God, and thereby made science possible; through the Enlightenment that gave us the ideas of human freedom. That's "the West" that we want to preserve.