The supernatural plays a major role in chapter 14 because it both saves Percy's life and keeps the plot moving forward by providing Percy with direction.
Firstly, Percy is able to take advantage of his supernatural lineage when he jumps into the Mississippi River. He is coming from a height at which an ordinary human being would be killed the moment they hit the surface of the water, but because Percy is the son of Poseidon, the water catches him gently before he makes a fatal impact. Not only that, but the water heals the poison from the Chimera's attack as well. Curious about his powers, Percy manipulates the water so he can make objects beneath its surface dry (for example, he sets a hamburger wrapper on fire under the water).
Secondly, Percy encounters one of his father's messengers beneath the water. The messenger tells Percy that his father believes in him and that his father wants him to go to Santa Monica beach. This gives Percy a lot of information he would not have otherwise been privy to, but the messenger, claiming weakness from being in river water rather than seawater, disappears before Percy can get more information from her. This is also supernatural, as the messenger is a representative of Poseidon, and her appearance to Percy is the result of magic.