This depends on which of the sniper's personas you think is the real him. The sniper shows two personalities over the course of the story. He shows the one whose eyes have "the cold gleam of the fanatic," but he also shows the one who is rattled and remorseful after the battle. These two personalities would have reacted very differently to the death of his brother.
You would hope that the remorseful personality would win out. If the sniper has any real humanity left, it would surely be activated by the death of his brother. He should feel shocked and horrified by what has happened. However, this horrible event might drive him deeper into fanaticism. He might become even more hardened as a way to protect himself from the emotional impact of having killed his brother. It is really impossible to know for sure. You should decide which of these sounds more plausible to you.