With railroad tracks, you can tip the skis and then end up in a skid if you don't let the skis turn your legs in the hip socket. So similarly, a quick pivot of the skis caused by the tip engaging won't work unless you let the skis turn your leg. In the gif, you can see that his upper body is not turning very much. The turn of the ski is rotating just the legs. How much of this he is letting happen vs actually assisting with a bit of active help to spin the ski around, I don't know.
So if you are tensing up your legs and being rigid throughout the dolphin turn, you won't get that quick pivot action. You will just keep going straight without the redirect.