The lunge whip is used properly by snapping it well behind the horse to motivate him.
If you can’t get them moving properly that way, walking out and behind them is next. If you have to strike the horse with the whip, you are doing something wrong.
A crack well behind them is all it sound take for them to advance gates. If they are just learning, perhaps a snap on the rear.
If you were to watch it done properly, you probably wouldn’t know the horse has hit. (and no way would it have any chance of hurting the horse.)
What it takes to train a horse depends on the horse. Without knowing what the horse the OP posted was doing, and without seeing what happened, I don’t know if there was abuse or not. But if you have a dominant horse, then the training might not be very pretty at times.
In turn, the laws are usually written in a way that allows ranchers and those training large animals considerable freedom. As I said, in most cases, no blood, no foul in the eyes of the law.
Branding cattle (or horses) isn’t pretty, but neither is it illegal.