In the story, the money turns to chips, horses to skeletons, and the house burns. What is Irving trying to say by using these descriptions?

Irving is trying to show the temporal nature of all things through this symbolism. Money turning to worthless chips, horses reduced to skeletons, and the destruction of a house by fire all point to one thing: Everything passes away, and all things are temporary in this life.

This symbolism is similar to other authors, who turn humans to dust, wilt flowers or plants, or use a number of other symbolic devices to demonstrate the passing nature of life. In any literary work, when an author reduces something to its simplest form or its base, that author is normally trying to display the simplicity and fleeting nature of that thing, whatever it may be.