Means in the whole world, by all parties of the world, world, Earth, all over the planet.
Is refers to the world in your set: all the surface of the world. Are multiple the expressions that contain " face of the Earth " both in a sense positive as negative. A species animal can disappear from the face of the Earth. Someone is it more kindly that exists on the face of the Earth. It is generally associated to States or extreme situations and found also in biblical sources.