I have been looking in some publications a projection where the globe appears as a marble (see attached example). However, I cannot find that projection in the ArcGIS list of available projections for the world.
"The World from Space" uses the orthographic projection. The "light rays" are hitting the globe as parallel "lines" from an infinite perspective (unlike say Stereographic where the perspective point is on the globe opposite the center point of the plane). Vertical near-side perspective has its perspective point at some distance above the globe, but not at infinity. It's more like the view from a satellite.