Let's start with the mood and atmosphere of the story as a whole. I would say that this story's mood is tense, dark, and violent. In a nutshell, the story is about a sniper that coldly shoots and kills three people. One of them happens to be his brother.
The opening paragraph helps to establish that mood by setting the story in the evening. Day is fading into night, so there is an actual darkness that accompanies the emotional darkness of the story.
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 all of the words that focus reader attention on darkness and dark times. "Twilight," "faded," "night," "darkness," "dim," and "pale" all highlight an ominous and oppressive feeling. The rest of the opening paragraph points readers toward the violence that is happening around the setting. A civil war is going on and guns can be constantly heard. Based on the opening paragraph, readers know that this story is going to be a dark and violent story.