The setting is June, 1922 in Dublin, Ireland. The country is engaged in a civil war at this time. The narrator doesn't get much into the politics of the war, but ends the first paragraph succinctly with, "Republicans and Free Staters were waging civil war." A thorough amount of background knowledge might help the reader to understand the causes and effects of the Irish Civil War, but foregoing that knowledge will not really affect the reader's general understanding of what the story is about.
That is to say, the story is about the violence of war and the odd nature of "brother against brother" in a civil war. The fact that it is a civil war is crucial to the understanding of the story. And being a civil war, it fought between two factions of the same country. Thus, the civil war is the backdrop for the place, time, and historical events that make up the setting. Without this general understanding of the setting, the story is just a couple of young guys shooting at each other. But knowing that it is a civil war, we (readers) gain a better understanding of what it means for people of a single country to be fighting each other. The final line underscores this absurdity. The sniper has shot his own brother. Perhaps it is his actual brother. Perhaps it means a fellow citizen, as in brothers of the same nation. In any case, the setting is crucial to understanding the violence of war what demarcates a civil war from other wars.