I'm trying to help a teacher friend of mine with finding a short story
"The Survivor", a novelette by Walter F. Moudy, previously identified as the answer to this question; first published in Amazing Stories, May 1965, available at the Internet Archive; you can also read it here.
In a post-war world there is a setup in which Soviet/Russian soldiers are required to fight against American soldiers in an arena
"My friends, many of you do not remember the horror of the Final War of 1998. I can recall that war. I lost my father and two sisters in that war. I spent two months in a class-two fallout shelter—as many of you know. There must never be another such war. We cannot—we shall not—permit that to happen.
"The Olympic War Games are the answer—the only answer. Thanks to the Olympic War Games we are at peace. Today one hundred of our finest fighting men will meet one hundred Russian soldiers to decide whether we shall be victorious or shall go down to defeat. The loser must pay the victor reparations of ten billion dollars. The stakes are high.
in which both sides have equal setup: a forest, a lake, etc.
The walls encircled an egg-shaped area which was precisely three thousand meters long and two thousand one hundred meters wide at its widest point. There were two large hills located on either side of the arena exactly midway from its center to its end. If you were to slice the arena crosswise, your knife would dissect a third, tree-studded hill and a small, clear lake; and the two divided halves would each be the exact mirror image of the other down to the smallest detail.
Given that he was the only survivor he has a sort of political amnesty in which he can do no wrong legally.
"I see the troops are beginning to stir. It won't be long now. Bill, while we wait I think it might be well, for the benefit of you younger people, to tell the folks just what it means to be a survivor in one of these games. Bill?"
"Right, John. Folks, the survivor, or survivors as the case may be, will truly become a Survivor. A Survivor, as most of you know, is exempt from all laws; he has unlimited credit; in short, he can literally do no wrong. And that's what those men are shooting for today. John."
The story ends with him watching a young girl next door get off the school bus;
Actually she's coming home from a movie date:
He was sitting in his room one evening when he saw Cassandra, the Martin's fifteen-year-old daughter, coming home with some neighborhood kid from the early movie. He watched idly as the boy tried to kiss her goodnight.
he walks to the neighbor's home, goes inside and, in front of the girl's parents follows the girl into her room and shuts the door, leaving the reader to assume whatever happens behind the door.
The Martins were still up. Mr. Martin was tying brightly colored flies for his new fly rod and Mrs. Martin was reading. They both stiffened when he entered without knocking—alarm playing over their faces like a flickering fire light. He didn't pause, but walked on up stairs without looking at them.
Mrs. Martin got to her feet and stood looking up the stairway without moving. In her eyes there was the look of a jungle tiger who watches its mate pinned to a stake at the bottom of the pit. Mr. Martin sat staring at the brightly colored flies on his lap. For a moment there was silence. Then a girl's shrill screams announced to the Martins that war's reality was also for the very young.