In "After Twenty Years," the narrator does not reveal the inner thoughts of any characters. The story is told in a very straightforward, objective manner. We only see what happens externally and hear what the characters say to each other.
This is typical of O. Henry's style, which often relies on plot twists and surprise endings to create dramatic effect. By limiting the reader to the external actions and dialogue, the suspense builds as we wait for the revelation of what will happen next.