The inciting incident of a story is the event or decision that begins a story's problem. I had a former teacher explain to me that everything before that incident is only backstory. Everything after that moment is the actual story.
If we apply this concept to "The Sniper" as a whole, then the backstory information is the opening paragraphs about the war going on and the fact that the sniper is in position as the day turns into night. At this point, the story is at peace. Everything is in balance. There is no conflict or problem to be solved.
As I said in the first paragraph, the inciting incident can be a decision that begins a story's problem. That is what happens in "The Sniper." The inciting incident in this story is when the protagonist sniper decides to light his cigarette.
He paused for a moment, considering whether he should risk a smoke. It was dangerous. The flash might be seen in the darkness, and there were enemies watching. He decided to take the risk.
The sniper could have chosen to not have his smoke, but he chose to take the risk. That single decision and action then propels the action of the story forward. From that moment forward, the sniper is under attack from an enemy sniper and an armored vehicle.
Placing a cigarette between his lips, he struck a match, inhaled the smoke hurriedly and put out the light. Almost immediately, a bullet flattened itself against the parapet of the roof.