The protagonist in the story, "The Sniper," is a young man, presumably just out of school, who is fighting in the Irish Civil War. Given that he is a young man who had the face of student but who had become "used to looking at death," the first implication is how much war can change a person. Here we have our protagonist, a young student full of hope and promise, becoming used to killing.
When the sniper eventually kills his enemy, he has the impulse to see his enemy's face.
When the sniper reached the laneway on the street level, he felt a sudden curiosity as to the identity of the enemy sniper whom he had killed. He decided that he was a good shot, whoever he was. He wondered did he know him. Perhaps he had been in his own company before the split in the army.
When the sniper sees his enemy, he sees "his brother's face." Given that this is a civil war, this could be taken literally. He literally killed his own brother. If "brother" means something more general, such as brother in country or in humanity, then the meaning changes just a bit, suggesting that he was related to this other young man by nationality, culture, or humanity. The overall implication is to show how war can divide a country, even a family. And with the sniper himself, the story shows how war can change a single young man into becoming used to looking at death.