There are a couple of ways to consider the words and phrases the author uses to describe the Republican sniper and what he is doing. We can discuss what he is doing and his reaction to what is happening to him.

The Republican sniper’s face is described as “thin and aesthetic,” which perhaps suggests a young, attractive man, with eyes that are “used to looking at death.” The sniper is depicted as a young soldier who has grown accustomed to his military responsibilities.

We get a good sense of what he is doing from the phrases “a bullet whizzed over his head” and “the sniper raised his rifle and fired.” The sniper is involved in warfare. He is in the dark, lying on a roof and shielding himself from bullets fired from other snipers shooting at him.

Another way to describe what he is doing would be to draw attention to his response to what is going on around him. The Republican sniper is initially calm as he eats his sandwich “hungrily,” takes a “short drought” of whisky, “place[s] a cigarette between his lips,” and “[strikes] a match.” His decision to light the cigarette, knowing that it could expose his position, lends some further insight into his callous, nonchalant disposition. Later in the story, the sniper is struck by a bullet and “drop[s] his rifle with a curse.” The pain is described as a “deadened sensation, as if the arm had been cut off.” Then, the pain in his right arm begins to feel like “a thousand devils.” One could argue that as the adrenaline from being shot wears off, the agonizing pain begins to set in.

Yet the Republican sniper’s sentiment about what he is doing changes. The author notes that the “lust of battle died in him.” The sniper begins “cursing the war, cursing himself, cursing everybody.” The sniper’s sentiment likely changes due to the “long summer day of fasting and watching over the roof” and of being under the “influence of the spirit,” suggesting that he may have grown frustrated due to lethargy and intoxication. Yet the inadvertent firing of his gun gives him a reality check that brings him back to focus.

In conclusion, a weary and drunken soldier seeks to escape to refuge but finds himself in another, more troublesome predicament.

His face was the face of a student, thin and ascetic, but his eyes had the cold gleam of the fanatic. They were deep and thoughtful, the eyes of a man who is used to looking at death.

The lust of battle died in him. He became bitten by remorse. The sweat stood out in beads on his forehead. Weakened by his wound and the long summer day of fasting and watching on the roof, he revolted from the sight of the shattered mass of his dead enemy. His teeth chattered, he began to gibber to himself, cursing the war, cursing himself, cursing everybody.

The Republican sniper, the main character in the story, is described as a young man with an innocent face, but he has the intense look of a soldier: 

His face was the face of a student, thin and ascetic, but his eyes had the cold gleam of the fanatic. They were deep and thoughtful, the eyes of a man who is used to looking at death. 

He is young. Consider that before the war, he would have had no knowledge of the kinds of violence one sees in a war. He would have been innocent, naive, and perhaps full of hope. The author is trying to show the transition from innocence to "a man who is used to looking at death."

When the author describes him, he uses the word "ascetic" which means having extreme self-discipline. The sniper is constantly fighting for his life. He has learned this self-discipline out of necessity. It is kill or be killed and this is why he does not hesitate in killing the woman. The "cold gleam" in his eyes is the result of intense anxiety and awareness of everything around him. The author wants to make it clear that this was once a young, innocent man ("face of a student") who has now become a killing machine. This shows the dramatic and traumatic effects a war can have on the psyche. 

When the sniper is shot in the arm, he endures the pain like a professional and plans his escape. But note that when he kills his enemy and the enemy hits the ground, the sniper does break out of his single-minded soldierly mentality. "His teeth chattered, he began to gibber to himself, cursing the war, cursing himself, cursing everybody." His humanism comes back to him for a moment. But the moment is fleeting. The violent sound of his revolver accidentally going off brings him back to that soldier's mentality. It is the violence that has conditioned him to become a soldier with "the cold gleam of the fanatic."