One of the most common morals of this story is that money and material possessions cannot substitute for love. There has also been a lot written about the Oedipal relationship between Paul and his mother. Since the father is basically absent, Paul takes it upon himself to make the money for the family and thus, assumes the role of the father, putting himself in an odd relationship with his mother. The moral here still has to do with love. If his mother and father had provided Paul with a loving family life, he would not have resorted to assuming his father's role and his death would not have occurred. So, certain psychological themes in addition to themes of love are often addressed.
If there is a hero in this odd type of fairy tale, it is Paul. He is the one who finds the treasure for the damsel in distress (his mother). But he does it by gambling. Since critics tend to focus on the mother's flaws and the father's inability to provide love or money, but rarely is anything said about the way Paul, his uncle, and Bassett go about getting the money. Betting on horses is legal, but this is beside the point. Paul's mother says she has no money because her husband has no luck. This is the wrong message to teach a child. Paul is lucky in the miraculous way he is able to pick winners. And he is generous to give his mother all of the money. So, he is heroic in this respect. But he has learned nothing about earning things. And this is his mother's fault.
So, the moral here is not necessarily that gambling is bad. Remember that Paul dies in the end. Gambling is a shortcut to success. So, this moral is that shortcuts such as these often lead to destruction in some way. Think of athletes who use steroids and businessmen who get into insider trading. These are corrupt strategies and are considered unethical or even illegal. If Paul had been taught that hard work brings money, maybe he would have gotten a paper route. He would have made less money, but the lesson would have been learned.