In the first method, he lets his board drag behind on a leash. If you want to go upwind, you can hold the board on an edge with windward arm while you control kite with your leeward arm and leg thrown over the lower LE.
I’d only try the second “pigtail” method if I broke a line and was somehow far from shore in offshore conditions or something where the potential added “efficiency” would offset the time it takes to setup. The first method is pretty useful for 99% of rescues where something g happened but you still have wind.