The story is told through a third-person omniscient narrator; meaning, someone not involved in the story itself, who knows the thoughts and feelings of all of the characters.  This helps us to understand the dynamics of the story a bit better; we understand the mother and father, and little Paul's obsession, and how all of them work together to produce the result.

I also provided a link to a discussion of the style of the story that is provided by eNotes; they have some great ideas.  They mention that the story starts off written almost like a fairy tale; we have a brief summary of a little family, told in distant, fable-like tones.  Instead of it being a super happy picture though, we see the discontented family where money is the ruling consideration, put above all things.  Through this fairy-tale style, we see the deterioration of Paul, through his attempts to be lucky, in order to win his mother's love.  It is also like a fable in that it ends in teaching an important lesson about life and happiness-that money can't buy happiness, and greed is a hungry animal that consumes all in its path.

Those are just a couple ideas on the style; I hope that helps!