The resolution, or denouement, of "The Interlopers" is the appearance of the wolves who are fast approaching the two foes made captive by a fallen birch tree. In the realization of their dire situation, the men have dispensed with their petty feud and resolved their conflict, but now face far worse foes, who bring death with them.

In this short story by Saki that is replete with ironies, the climax occurs after the dramatically ironic declaration of each foe that his men will arrive before the other's and fatally resolve the longstanding dispute over land with the death of this other man.
However, as they lie victims to the forces of an indifferent Nature, 

In the pain and languor that Ulrich himself was feeling, the old fierce hatred seemed to be dying down.

He, then, tells Georg that theirs was a fair compact, after all. So, if his men arrive first, he will have Georg helped before he is since his heart has changed and he no longer feels enmity toward Znaeym. In fact, he goes so far as to now consider Znaeym as his guest, and even asks George to be his friend. This change of heart in Ulrich means that Georg is no longer an "interloper." Moved by this offer of friendship, Georg agrees to end their feud. This resolution to the feud between the men as the falling action of the plot of Saki's story now gives rise to a bitter and dramatic irony, as with their shouting to alert their men of the predicament in which they now lie, Ulrich and Georg have summoned new interlopers, the hungry wolves of the Russian forest.

Thus, the sinister approach of the wolves which causes "the idiotic chattering laugh of a man unstrung with fear," marks the denouement of the story as Georg, unnerved by Ulrich's hysterical reaction, asks, "Who are they?" and Ulrich replies, "Wolves."