I think a moral of the story is about the dehumanizing effects of war. War itself removes the humanity from people and turns them into mere targets to be eliminated. Liam O'Flaherty helps sell this idea of war being impersonal by never naming any of the characters. They are simply described as this sniper, that sniper, an old woman, etc.
In addition to characters having no names, the war dehumanizes the characters by making them all equal targets of opportunity. To the sniper, it doesn't matter if his target is young or old. It doesn't matter if his target is man or woman. It doesn't matter if his target is armed or not. Each person that he sees through his scope is a target of opportunity. The real shock to the young sniper is that his desensitized attitude causes him to kill his own brother.
I would say that a moral message in the story is to be aware of how war tends to create an attitude of impersonal distance from your fellow man.