There's a fine line between dreams and delusions. There's nothing wrong with having dreams, of course, but they do need to have some kind of realistic foundation to them, otherwise you'll end up sorely deluded. The protagonist of the story hopes to make it big as a journalist in New York. That's a perfectly fine, realistic ambition. However, he thinks it's going to be a cinch to get his foot in the door. All he needs to do is come up with a quick article on sparrows in Madison Square and—hey presto!—he'll soon be holding down a regular job at the Sun newspaper for the princely sum of $80 a week. This is not a dream; it's a delusion.

The tramp was robbed of $15 when he first came to the city in search of easy money. Metaphorically, though, he was robbed of his dreams by his delusions. Now it's the young man's turn.

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.