If you are moving the sun/projector, you'll get some aliasing effects on the shadows based on the size of the shadow map, the distance of the sun from the scene and the fov of the projector. You can try to decrease the fov and/or the distance to increase the accuracy. Apart from that, there's nothing you can do with this kind of shadows. I haven't seen anything in the video that i found surprising, but the quality was pretty low though. Maybe you can upload the video that shows the problem in more detail? Maybe i'm just not sseing it.
If it still doesn't work out, just don't move the sun...