"Mammon and the Archer" is an unusual type of story for O. Henry because he is dealing with the old rich and nouveau riche of the late nineteenth century. His main character, the protagonist Anthony Rockwall, is a stereotype common to fiction of the times. Rockwall is a self-made millionaire who admits:
"I'm nearly as impolite and disagreeable and ill-mannered as these two old Knickerbocker gents on each side of me that can't sleep of nights because I bought it between 'em."
The English must have had this stereotyped impression of wealthy Americans. Arthur Conan Doyle presents several such crude, aggressive characters in his Sherlock Holmes stories.
Rockwall can't get into high society, but he wants his son to do so. Why? His son will be a symbol of his own success, just like his house and his yacht. Rockwall actually hates the old rich. He refers to his snobbish neighbor, the aristocratic clubman, G. Van Schuylight Suffolk-Jones, another stereotype, as a "Stuck up old statuette of doing nothing!"
Young Richard Rockwall is another stereotype character, a boy who has been deliberately spoiled in order to make him into a gentleman, i.e., a person who never has to work with his hands. He has been sent to one of those all-male colleges where most of the time is spent drinking and playing rather than on studies. He is encouraged to be a fop and a wastrel. He doesn't have to worry about earning a living because his father will leave him millions and may get him a phony job as a stock broker or member of a board of directors just for the sake of appearances. A real gentleman should not really have to work. Contemporary fiction was full of such characters who had some vague connection with some firm in the city but never seemed to have to go there.
Naturally Richard has fallen in love with a society girl who is also a stereotype. She is always referred to as Miss Lantry, as if she is too superior to be called by her first name by such persons as Anthony Rockwall, Richard Rockwall, or Aunt Ellen. Miss Lantry is available as a bride to any young man who can offer her the lavish lifestyle to which she has become accustomed. She will be sold to the highest bidder, like so many of the upper-class girls of her time.
O. Henry seems to be illustrating the thesis that there is no such thing as real love, at least at the highest social level. His reference to "a fat boy without any clothes on shooting arrows around with a bow" is tantamount to saying that love is nothing but an illusion, a myth. This is in direct contradiction to the theme of his story "The Gift of the Magi," to name only one example.
Rockwall is proud of his son but doesn't appear to love him, and Richard doesn't appear to love his father either. Richard is mainly attracted to Miss Lantry because she symbolizes the upper class. He tells his father:
"For one thing...[money] won't buy one into the exclusive circles of society."
But his father knows better and proves him wrong by spending some of his money to create a traffic jam that will give his son the time to propose marriage to Miss Lantry and for her to accept. The marriage will probably endure as well as one based on "love" because both these spoiled young people will be able to live in luxury and move in the best circles for the rest of their lives.