What could the broken tree represent in Saki's short story, "The Interlopers?"
This is a great question. Sometimes in short stories, we forget to look for meaning in symbols. The broken tree means that the men were the true interlopers, which is ironic, because this idea probably never crossed their minds.
Both men, Georg and Ulrich, believed that the other man was the interloper. In fact, according to the text, Ulrich was out with his men to see if Georg was there. He wished to find Georg at the other end of his gun to kill him for trespassing on his land. Ulrich does meet Georg, but something unexpected happens. A tree falls on them and the men are pinned down. Finally, wolves come, instead of men, and the presumably die.
In view of these points, it seems that nature made it that each man got his wish for the other. Both died as interlopers.