In "The Interlopers," the protagonist hates the antagonist. How do we know this?

Now this is a very interesting question, because the way
you have worded your question seems to infer that the protagonist and antagonist are
respectively Ulrich von Gradwitz and Georg Znaeym. I would actually beg to differ. I
personally think that the protagonist in this excellent short story is nature and that
the two feuding men are the antagonists. You might like to consider the way in which the
violence of nature is described in the scene when a tree falls on top of them
both:

And
before the moment of hesitation had given way to action, a deed of Nature's own violence
overwhelmed them both. A fierce shriek of the storm had been answered by a splitting
crash over their heads, and ere they could leap aside, a mass of falling beech tree had
thundered down on
them.

Nature itself is
described as a character that shows its anger at the way in which these two interlopers
have ingressed on her territory. The petty nature of the quarrel between the two men is
thus highlighted, as the stretch of land that they have argued about so fiercely doesn't
really belong to either of them, but to Nature itself, and Nature is clearly not pleased
by the arrogance of both men and their claims to what is rightfully hers. The violence
of Nature makes this perfectly clear.