The author probably chose to do this for a few reasons, in my opinion. First, readers generally understand and empathize with the protagonist of the story; in this case, that would be the sniper. We understand his struggles, his motivations, his thoughts, etc., all because of the author's use of first-person narration.
Also, I have never served in the military, but I believe this is how soldiers are trained to view their adversaries: they are the enemy and therefore must be eliminated, if you don't kill them then they will kill you. I believe soldiers might realize that if they begin to imagine their enemy as a real person, then it'd be much harder to kill that person. Better to "dehumanize" the target.
Finally, I think that this allows us as readers to not even consider the possibility that the enemy is his brother. By keeping this other rifleman as vague as possible, we never would guess that they are related.