What could be the experience of "The Sniper" from the point of view of the antagonist?
I assume that you are thinking that the enemy sniper is the antagonist in this story. If so, I think that his experience of the story would be identical (in all important ways) to the experience of the protagnoist. I think that the author means to show that the two sides in this struggle are identical -- that the people have no reason to be fighting one another.
There are differences, of course. The enemy sniper would feel angry, I imagine, when the sniper kills the old woman or the soldier in the turret. But these are not the important things. Throughout the story, the enemy sniper would feel the same sorts of tensions as the sniper who is the protagonist in the story. He would feel nervous and he would feel like a fanatic. At the end of the story, (we'll assume he's alive when the other guy turns him over) he would also feel the same sort of horror when he realized that it was his brother who killed him.
I think the author is trying to make us see that the two snipers are essentially the same. Because of that, I think they would have very similar experiences in this battle.