Of course God is God of the entire world. The reason for focusing on the concept of the God of Western Tradition is that it is the concept of God most familiar to us in the West. And this is no doubt because the Biblical God had the biggest impact historically in Europe and America over the last two millennia, up until relatively recently, although the specific theology of the Christian God (the Trinity for instance) is not part of the definition that Robin gave
If god is the god of the entire world why would this revelation be only be to some people.