Why does the sniper shoot the man in the armored car and shoot the woman?
This short story is set during the Irish Civil War. The two warring sides are the Republicans and the Free Staters. The protagonist, "the sniper," fights on the Republican side. As a sniper, in this case, he is on his own.
After eating a sandwich, the sniper lights a cigarette and his enemy, a different sniper for the Free Staters, sees the smoke and fires at him. At this point, the enemy sniper knows his position.
The armored car approaches. An old woman informs a soldier in the turret of the armored car of the sniper's (protagonist's) position. The sniper shoots the man in the turret when he is in view. He needs to do this before that soldier can attack him or inform other soldiers of the sniper's position. Then the sniper shoots the old woman to prevent her from informing any others.
The sniper kills these two in order to protect himself. As the narrator notes, the sniper has become "used to looking at death." He understands that if he does not kill the enemy, he will be killed.