That particular projection is called "Orthographic". Of course, you don't have to use Celestia to view a map that way. Here's a similar view using G.Projector. Like Celestia, though, G.Projector needs the input map to be an Equirectangular projection (also called Plate Carrée). I used Paint.net to overlay the regional political map on an earlier full-surface map.

Click image for larger version. 

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