Why doesn't von Gradwitz want witnesses to see what he has planned?
Ulrich von Gradwitz doesn't want any witnesses around when he kills Georg Znaeym. In other words, he aims to kill his rival if he catches him alone. Privately, Ulrich isn't interested in just apprehending his enemy; he means to kill Georg if the opportunity presents itself, and in the event he gets his chance, Ulrich doesn't want to be held accountable for the murder.
This is part of the reason von Gradwitz orders his men to lie in wait at the crest of the hill while he ventures further down the steep slopes. As luck will have it, he does come face to face with Georg. The text tells us both men are not entirely unhappy with this state of affairs. Each man cherishes hate and murder in his heart, and each is ready to "give full play to the passions of a lifetime." As the narrator relates, things don't turn out the way each imagines it will.
An unforeseen catastrophe sees both men pinned down by the branches of an enormous beech tree. The ending of the story is ironic, and the text suggests both men may die together at the hands of wolves.