Using a skinning knife works best. The one in the video is a bit different, but this one is a good knife:
The skin is rather tough, so you are running your knife right up against it. It is mostly a "feel" thing... practice will help. Cutting the little finger holes like in the video works great.
18.5 WSM, Green Weber Genesis320, Cast iron firepit(w/grill), and a Copper Weber 22" OTS