In "The Sniper," like the famous short story, "The Most Dangerous Game," the climax of the story occurs at the very end.
The difference between the two is that there is a small amount of resolution in "The Most Dangerous Game," where in "The Sniper," there is none.
The conflict here that is most significant is not the battle between the Republican army and the Free Staters. It is the conflict between the two snipers, both of whom are very talented.
As the first sniper is located and fired upon by the other sniper, this is where the most exciting conflict builds—man vs. man. Each sniper is pitted against the other, trying to be smarter or more skilled in killing his adversary.
In "The Sniper," the first sniper finally kills his opponent. The only falling action here is in the time it takes the sniper who has survived to reach the street and check to see the identify of this skilled sniper, who he admires. The conflict is over in the killing, but there is no resolution in my mind. The sniper turns over the body, sees his brother's face, and the story stops. Any resolution in the story is left with the reader as he/she tries to sort out "what just happened?" and imagine how the sniper feels now—what he will do next.
Please note: not all stories have a resolution.