The protagonist is a term that is used to describe the main character of a short story, who is normally opposed by the antagonist. In this short story, as with all of the Sherlock Holmes stories, it is clear that the protagonist is Sherlock Holmes himself. It is he, after all, who does all of the thinking and deducing to solve the mystery that is presented before him, and it is he who faces John Clay, the antagonist, at the end. Note what he himself says after the case has been solved and he is thanked by Mr Merryweather:
"I have had one or two little scores of my own to settle with Mr. John Clay," said Holmes. "I have been at some small expense over this matter, which I shall expect the bank to refund, but beyond that I am amply repaid by having had an experience which is in many ways unique, and by hearing the very remarkable narrative of the Red-headed League."
The way in which Holmes acknowledges that he has had some emnity with John Clay identifies Clay as the antagonist of this short story and himself as the protagonist. He has, after all, solved the case again and prevented a robbery from occurring. Even though the story, at the beginning at least, mostly involves Mr Wilson, it is clear that it is always Holmes who is acting to solve the mystery and bring about a happy conclusion, making him the protagonist.