Since Tom Benecke is virtually the only character in the story, the conflict would have to be described as one of man against himself. The protagonist is Tom Benecke. The antagonist is Tom Benecke. His first struggle with himself occurs when his precious yellow sheet blows out the window and gets stuck against the building just out of reach. One part of Tom tells him to forget about it. The other part tells him that he should try to retrieve it because he has worked so hard to obtain the information.
But just the same, and he couldn't escape the thought, this and other independent projects, some already done and others planned for the future, would gradually mark him out from the score of other young men in his company. They were the way to change from a name on the payroll to a name in the minds of the company officials. They were the beginning of the long, long climb to where he was determined to be, at the very top. And he knew he was going out there in the darkness, after the yellow sheet fifteen feet beyond his reach.
Then when Tom is out on the ledge inching his way towards his prize, he has to struggle with himself not to lose his nerve. One part of him is ready to panic. The other part is refusing to yield to his emotions and also steadfastly refusing to look down. But when he finally makes it to within reach of the yellow memo sheet, he finds that he cannot get a grasp on it without looking down at least for an instant.
He saw, in that instant, the Loew's theater sign, blocks ahead past Fiftieth Street; the miles of traffic signals, all green now; the lights of cars and street lamps; countless neon signs; and the moving black dots of people. And a violent instantaneous explosion of absolute terror roared through him. For a motionless instant he saw himself externally--bent practically double, balanced on this narrow ledge, nearly half his body projecting out above the street far below--and he began to tremble violently, panic flaring through his mind and muscles, and he felt the blood rush from the surface of his skin.
The sight almost causes him to fall. He realizes the terrible position he is in. His only hope of saving himself from a horrible death is to keep control of his emotions and force himself to inch his way back to his apartment window. The struggle of man against himself is infinitely harder now that he has looked down and seen the dizzying spectacle of Manhattan at night, with pedestrians only little black dots and lights constantly changing shapes and colors. Everything is in motion. All the traffic lights along Lexington Avenue are now green--but at any second they will all turn red, and the effect will be disorienting, possibly even hypnotic. He has to fight to keep his sanity and fight against the impulse to get it over with--to let himself go flying backwards off the ledge and down to his death. He even imagines himself already dead on the street below.
Then when he finally forces himself to take the necessary steps back to his window, he finds that it has slammed shut. It is an old building with windows that haven't been maintained properly for many years. It was hard enough to open the window from the inside, where he could give it is strong jolt with the palms of both hands; but it is out of the question to try to open it from the outside. He can't stand there for four hours while his wife is enjoying the movie at Loew's theater. He has to break the glass, then knock out all the jagged shards and climb through. Here he has to force himself to land a blow hard enough to break the glass, while at the same time another part of himself is telling him that he will lose his balance if he tries it. He might break the glass and at the same time go falling backwards to his death.
So the protagonist manages to conquer the antagonist. Tom Benecke keeps his nerve and saves his life, although he has learned from his experience that he was crazy to risk it in the first place.
An antagonist can be different things in a story - a villian (the most commonly thought of), a competitor or rival (not necessarily villainous), or a major threat or obstacle the protagonist has to overcome, even though it might not necessarily target him or her. This last meaning of antagonist is the one which is applicable to the short story "Contents of the Dead Man's Pockets." Within this story, the antagonist can be two-fold - both the harsh setting on the ledge with the wind buffeting his body and Tom's own feelings of terror and panic which he must battle to regain the safety of his living room. The phrase "He is his own worst enemy" is applicable in this short story by Jack Finney.