Tone is the attitude of a writer toward a subject. Tone is generally conveyed through the choice of words that the author uses for a particular subject.
"The Sniper" is a story about civil war. It is a story that shows the horrors and brutality of war. O'Flaherty is not romanticizing war in this story. His word choice conveys his overall pessimistic and negative attitude about civil war. Let's look to the first paragraph for an example.
The long June twilight faded into night. Dublin lay enveloped in darkness but for the dim light of the moon that shone through fleecy clouds, casting a pale light as of approaching dawn over the streets and the dark waters of the Liffey.
Notice the night setting and the emphasis on darkness. The moon is shining, but it doesn't even have full brightness, because of the cloud cover. It's literally a dark setting about a dark and negative topic. O'Flaherty's description of the sniper further deepens the pessimistic tone.
They were deep and thoughtful, the eyes of a man who is used to looking at death.
The Republican sniper is not new to killing. He's experienced at dealing death through a rifle scope. The pessimistic tone continues once the sniper begins fighting for his life. Enemy combatants are not described or named. This creates detachment for readers and the sniper. The old woman, soldier, and enemy sniper are simply faceless targets. It's as if O'Flaherty is attempting to show readers how war dehumanizes people. The ending of the story is the most pessimistic and negative part of the entire story. Readers realize that while the sniper succeeded in securing his own survival, it was at the cost of killing his own brother. War is bad, but civil war tears apart families.