Well how else do you propose they do it? The two methods I know of are 1.) using an electric probe to knock them out cold, then hoisting them up and cutting the throat to drain the blood. And 2.) using a bolt gun to the head to kill it right away, and then hoisting them up and cutting the throat to drain the blood.
It's awful. And it's sad. But there is no other way to do it that is as fast and effective that will keep it fit for consumption. It's not perfect, but it's about the best they can do.
Edit: Yes to everything said above me! Mexico horse slaughter is absolutely brutal. Better to do it here where it is regulated.