I was using the term "western history" with respect to its conventional definition:
Western world - Wikipedia, the free encyclopedia
So no, ancient Greece doesn't matter in this case.
You quote a source declaring the Greco-Roman era as being "Western History", and then say Greece doesn't matter. Your declaration doesn't fit your source. Is there an on-off switch on peoples minds?
Let me quote you another source with dates attached, which does include Greece. Outline of History - The Flow of History This may allow you to reactivate the mind switch. Greece is very much part of the Western History, and of Western philosophy, and of Western democratic politics, and of Western war. For the Seals training is modeled on the Spartan model. Our mathematics and science draws on Pythagerus and Archimedes, and while they may have had contacts with Egypt and the mysteries of God and the prophets, they had no access to Pauline "Christianity".