Why do the characters in "The Interlopers" by Saki hold a grudge against one another?
The central conflict in "The Interlopers," by H. H. Munro (Saki) is man versus man, though certainly man versus nature also plays a role in this story. The short answer to your question is that the two main characters hold a grudge against one another because of some land.
Ulrich von Gradwitz is the owner of a significant amount of richly forested land, "well stocked with game." On the outskirts of his vast holding is a "narrow strip of precipitous woodland." Though this land is not replete with game for hunting, von Gradwitz guards it more closely than any other plot of land he owns, and this is why.
A famous law suit, in the days of his grandfather, had wrested it from the illegal possession of a neighbouring family of petty landowners; the dispossessed party had never acquiesced in the judgment of the Courts, and a long series of poaching affrays and similar scandals had embittered the relationships between the families for three generations.
Though the courts had determined, three generations ago, that the von Gradwitzes owned the land, the family of Georg Znaeym never accepted the court's decision and continued to hunt on the land (which is, of course, considered poaching if the land does not belong to the hunter).
The neighbour feud had grown into a personal one since Ulrich had come to be head of his family; if there was a man in the world whom he detested and wished ill to it was Georg Znaeym, the inheritor of the quarrel and the tireless game-snatcher and raider of the disputed border-forest.
If the current heads of these two families had not made the feud personal, things might have reverted to normal; however, the men hold "personal ill-will" against one another and the feud continues.
[A]s boys they had thirsted for one another's blood, as men each prayed that misfortune might fall on the other.
As the story begins, the two men are hunting in the disputed land, and they are hunting one another.