The story is written mostly as narration, but there are descriptions and dialogues also. It's the third-person  narration, the story-teller being none of the personages but a full observer. It's possible to state that this type of narration was chosen to make the story more objective and free from personal attitide.
From the point of view of the composition the text comprises the following parts: it has no exposition as the text immediately starts from the events - the whole family at home at chess and knitting; so the plot is up to the climax - the scene where the man from 'Maw and Meggins'  informed Mrs. and Mr. White about the amount of compensation according their son's death and the father realizes that it's exactly that amount of money that he wished to monkey's paw; then goes an anticlimax where the narrator tells us about the parents' grief; at last goes unexpected scond climax when poor mother realises that there're two more wishes to monkey's paw and she wants to raise her son from the dead. This second climax lasts up to the end of the story keeping readers' attention.
I've managed to notice that according to the structure developing the colours and characters' mood develope. It becomes darker and more gloomy. Maybe the author uses this trick to create the reall readers' tension as it's suitable for horrors.