How does the narrator reveal the thoughts and feelings of the two men?

In this story, Saki uses a third person omniscient narrator. This is the "all knowing" narrator. He is able to give the reader any information about the setting, plot, external world, and also the characters' thoughts. 

In the first paragraph, the narrator describes the setting and shows Ulrich patrolling his land. The narrator gives us the additional insight that Ulrich is not hunting an animal. He is hunting a human foe. 

After giving the backstory...

In this story, Saki uses a third person omniscient narrator. This is the "all knowing" narrator. He is able to give the reader any information about the setting, plot, external world, and also the characters' thoughts. 

In the first paragraph, the narrator describes the setting and shows Ulrich patrolling his land. The narrator gives us the additional insight that Ulrich is not hunting an animal. He is hunting a human foe. 

After giving the backstory of the feud between the two families, the narrator notes how Ulrich and Georg hate one another so much that they both consider murder. The narrator directly tells us what Ulrich is thinking: 

If only on this wild night, in this dark, lone spot, he might come across Georg Znaeym, man to man, with none to witness—that was the wish that was uppermost in his thoughts. 

And when they meet, he adds: 

The two enemies stood glaring at one another for a long silent moment. Each had a rifle in his hand, each had hate in his heart and murder uppermost in his mind. 

However, both men hesitate, the lightning strikes, and they are trapped beneath the tree. After pointlessly threatening each other while pinned, the narrator notes that Ulrich has a moment of empathy for his enemy: 

. . . nevertheless, the wine was warming and reviving to the wounded man, and he looked across with something like a throb of pity to where his enemy lay, just keeping the groans of pain and weariness from crossing his lips. 

Georg initially refuses. The narrator adds that the idea of a truce begins to develop in Ulrich's mind. Ulrich tells Georg his men will not harm him if they arrive first. Georg reciprocates the gesture and the truce is made. For the remainder of the story, the characters' thoughts are largely communicated through dialogue. But in the moments leading up to the confrontation, the narrator provides some key insights about the thoughts the men have and how those develop into thoughts of reconciliation.