How does the sniper transform into a human being?
The sniper initially is characteristized animalistically. His actions are portrayed as instinctual. The author states "...his eyes had the gleam of a fanatic." Fanatics are not thoughtful but singlemindedly focused on one thing, reacting without logical thought.
In the next paragraph, the sniper eats a sandwich "hungrily" and inhales his cigarette "hurriedly." These actions portray a character who is reacting to circumstances without thoughts or emotion.
When waiting out the other sniper, the protagonist exhibits the ability to think through his predicament when he raises his cap on his rifle's muzzle to locate the other sniper. This type of thought begins to transform the main character from merely reactionary to thoughtful.
When he shoots his enemy and watches him fall to the ground, the sniper exhibits emotion and the tranformation begins. "He became bitten by remorse" and "he began to gibber to himself, cursing the war, cursing himself, cursing everybody." These behaviors show his very human emotions to having killed another man which will only increase when he later discovers the identity of the other sniper.