This story is unusual in that it really only has one character – and that's our narrator, the librarian. Sure, he mentions a few other people in his telling of the philosophic history of the Library, but none of those individuals is very important to the story. They all tend to represent general movements or tendencies in historical thought, rather than taking on an important role in the development of the plot.
So, by default, our narrator is the story's protagonist. He is, after all, the one character that we empathize with – we feel a little sorry for the poor old guy, who has no other company than his books. We'd like to give him a hug.