Like it or not, the "west" has a cultural common ground (Indo-European derived, chiefly greco-roman, gaulic and germanic cultures which were not isolated from each other as you would imply), and more importantly a religious common ground in judeo-christian religion and morality. Poland helped Austria against the Ottoman invasions because of this common ground, and predominantly anglo-saxon Americans read Homer's poetry because of this common ground.

From the viewpoint of a person outside "the west" under both grounds, it's a clearly recognized entity. There may be blurred contours. That doesn't invalidate the existence of such an entity.