That video includes photo-realistic clouds in the sky. Is it possible to add clouds like this in ArcGlobe?
The clouds on the animation seem to be on an vertical plane at a given distance (when the "plane is turning, there is some sort of acceleration of the closest clouds, but far and close clouds don't seem to be moving with respect to each other when the "plane" is approaching.) So, instead of trying to change the background (which doesn't seem to be possible), I propose the following workaround :
build a very tall textured 3D object with a 2D sky image for the texture. http://resources.arcgis.com/en/help/main/10.1/index.html#//00q80000000m000000 as you probably know. If it is far enough from the position of your plane, and you don't look too high above the horizon, you can have the same result as in the nice movie you've shown.