How does Ulrich and Georg’s experience of being trapped together advance the plot of the story?

The trapping of the two enemies beneath a mass of tangled, heavy branches on the disputed land advances the plot because the shared life-threatening dilemma with which they are confronted prevents any physical reaction and gives them cause to evaluate the significance of their feud.
For it is only because they are forced together "by a deed of Nature's own violence" that the two men communicate. Relieved that they are still alive and greatly annoyed at their plight, the foes lash out at each other. Each man boasts that when his men arrive first the other will suffer death. Yet, each speaks "with the bitterness of possible defeat before them." This underlying fact causes the men to ponder more their predicament in relation to the significance of their enmity. After some time in which no rescue party arrives for either of them, Ulrich suddenly asks his old foe if he can catch a flask containing warm wine, adding, "Let us drink, even if tonight one of us dies." Georg refuses at first, but after Ulrich offers to end their feud if Georg will agree, Georg reflects on this offer.

Georg Znaeym was silent for so long that Ulrich thought perhaps he had fainted with the pain of his injuries. The he spoke slowly and in jerks. "How the whole region would stare and gaggle if we rode into the market square together. . . . And what peace there would be among the forester folk if we ended our feud tonight.

Both men reflect upon the changes that this "dramatic reconciliation" would bring. Each prays a silent prayer that his men will be the first to arrive so that he can demonstrate his magnanimity to his former foe who has now become a friend. Unfortunately, however, the ironic reversal of fate ends their hopes.