At first glance, it may seem as though Sandel, the fighter who opposes Tom King, is the antagonist of the story. Roughly two-thirds into the story, it even states
The third round began as usual, with Sandel doing all the leading, and delivering all the punishment.
However, even though Tom King does not fight back, it turns out Sandel is not the true antagonist of "A Piece of Steak," as evidenced by this quote a little bit further on:
His gloves had already been removed, and Sandel, bending over him, was shaking his hand. He bore no ill-will toward the man who had put him out and he returned the grip with a heartiness that made his battered knuckles protest.
"A Piece of Steak" is atypical of many stories because it does not have a person who is the antagonist; instead, the antagonist is simply old age. In the beginning of the story, Tom King sees Stowsher Bill crying in the dressing room and cannot fathom why such a prized fighter would be bent over in tears.
As the story continues, however, it becomes evident that Tom King is no longer in his prime. Though he was once the best fighter in the world, age and time have caught up to him. Toward the end of the story, it states:
King did not attempt to free himself. He had shot his bolt. He was gone. And Youth had been served. Even in the clinch he could feel Sandel growing stronger against him. When the referee thrust them apart, there, before his eyes, he saw Youth recuperate.
This shows that it doesn't really matter who the opponent is—youth will always prevail. The fact that the word "Youth" is capitalized throughout the story shows that it holds a place of reverence, and Tom King realizes that he has lost his somewhere along the way. It is his turn to become the once-prized fighter, bent over in the dressing room in tears.