The theme of this story is that dreams do not come true.
We see this first of all in the story of the narrator. He comes to New York City, sure of how he will get his start in the news business. He writes his article about the sparrows, but is rejected and now has no real plan for what to do next.
Then, we see the theme even more clearly in the story of the bum that he meets. The bum actually did sell a story about the sparrows but it didn't do him any good either because his money was stolen. As it turns out, whether or not you sell your story, you still don't make it. That shows us that dreams just don't come true.