To be honest with you, I don't actually see the either sniper as symbolic characters. Symbols are concrete expressions of abstract or figurative ideas. I just don't see the snipers as anything other than what they are in the story--parts of a war. A symbol can't stand for what it actually is.
The power of the story is derived not from any symbolic representations, but from the blast of situational irony the reader gets at the end when the protagonist looks at the man he just killed and sees that it is his brother. Perhaps you could say that this act is symbolic--representing the fact that war and violence bring unpredictable destruction to the lives of those that are involved in it.
In the short story, The Sniper by Liam O'Flaherty, the sniper is the protagonist and is used as a symbol for several things. He symbolizes the terrible price of a civil war in Ireland where families were often divided with members on both sides of the fighting. The ending where the sniper turns over the soldier he has killed and discovers the body of his brother brings the symbolism home all too clearly. The sniper also symbolizes the destruction such a war can cause in a society which will suffer the aftereffects for years to come where even an old woman becomes an enemy to kill. The sniper also symbolizes the changes a person must make in warfare. He has the face of a student which he probably was before the war, but is now killing his fellow human beings as a soldier and for his own survival.