For most of the story, the sniper is on the defensive. Early in the story he lights a cigarette and gives away his position to the enemy sniper. The sniper does manage to relocate, but he knows that any subsequent actions will re-alert the nearby enemy sniper. Despite knowing that firing his rifle will once again give away his position, the sniper shoots two people. As a consequence, the sniper gets shot in the arm by the enemy sniper. The sniper is very much in a defensive posture at this point. He can't lift his rifle properly any longer, and the enemy knows his location. He is a dead man unless he finds some way to go on the attack.
In order to get out of his difficult situation, the sniper manages to fool the enemy sniper into thinking that he is dead. That little bit of subterfuge is the turning point in the story, because it finally allows the protagonist to go on the offensive. He has successfully fooled his enemy, which then allows the sniper to kill his opponent. The switch from being the hunted to the hunter is why that part of the story is the turning point.