When the sniper kills his enemy, he decides to to have a look at his victim. He considers the possibility that he might know this enemy sniper.
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. He decided to risk going over to have a look at him.
The final line of the story indicates that the sniper looked at his enemy and saw "his brother's face." This could be quite literal. Given that the sniper's army split as the civil war developed, it is possible that his brother had become his enemy. But it is also could refer to countrymen as brothers. This is why civil wars are often described as wars of "brother against brother." In either case, the implication is that the sniper knew his victim (as his brother, a friend, acquaintance, or countryman). The shock is that he knew (in any of those interpretive senses of "brother") the man he killed and this shock speaks to the insanity of war.