When we think of conflict there are two kinds that we refer to in the study of literature: internal and external. Internal conflict is normally used to refer to some kind of internal struggle, for example a climber who needs to physically and mentally urge himself on to reach the top of a mountain. External conflict is referred to when the conflict is between a character and another character.
Clearly, then, "The Sniper" shows us an example of external conflict, as the story presents us with a grim fight to the death between to snipers from rival sides of the Irish Civil War, that split the country apart, and also many families, as some family members took opposing forces. Consider the following paragraph:
The sniper lay for a long time nursing his wounded arm and planning escape. Morning must not find him wounded on the roof. The enemy on the opposite roof covered his escape. he must kill that enemy and he could not use his rifle. He had only a revolver to do it. Then he thought of a plan.
This then presents us with the title character of this excellent short story working out how to resolve the external conflict he faces and kill his opponent, thereby ensuring his escape.