The point of view in "The Sniper" is third-person subjective. (Third-person narration never uses "I," "we," or "you.") The third-person subjective narrator describes the events as they appear and gives the reader information about the sniper's feelings (thus, it is subjective). Since the narrator focuses on the feelings of one character, the sniper, we can also call this type of narration (point of view) third-person limited because the narrator limits psychological insight to one character. And although the third-person narrator is removed from the world of the story, describing the events as if from above, third-person narration can also delve into the mind(s) of character(s). In this story, the narrator describes things from above, so to speak, but also gets into the mind of the sniper, thus making the subjective insight limited to the sniper. In this case, the point of view is outside the world of the story, looking on, but also gets into the world of the story by getting into the mind of the sniper. After killing the enemy sniper, the sniper (main character) is described by this point of view, the third-person point of view looking on and then getting into the mind of the character: 

The sniper looked at his enemy falling and he shuddered. The lust of battle died in him. He became bitten by remorse. The sweat stood out in beads on his forehead. 

The first sentence describes the scene. The second and third sentences describe an emotional change in the sniper. The fourth describes a physical fact that is observable of the scene.