The grid won't be distorted, only the one face. If I look again at the image at the top, I would say there almost isn't a pole. The face of the sphere will not move. The image distorted will shift instead to give the appeal of a rotating sphere, kind of like a side view of the earth spinning (assuming no tilt of the axis, just perfectly straight). Also the sphere would be restricted to either pure vertical or horizontal movement at any one time; not both. Hope that clears it up.

PS: Made a little picture: Say I wanted to wrap this to the sphere, but the tanks could still move:



Obviously the tanks would be moving on the flat square bitmap, but projected on the sphere as though on the sides.