Local Legend
Because Princess Academy is set in a place with such a rich storytelling tradition, it makes sense that the writing style would mimic that of a well-worn local legend. This becomes especially apparent when the book goes into detail about Mount Eskel's culture, like when the girls come home for the spring holiday:
That afternoon, the sounds of song greeted them at the outskirts of the village. Dozens of voices carried the melody, and slapping drums and clapping hands thrummed the beat. The girls recognized the tune and rhythm of the empty barrel dance, the first dance of spring holiday. (11.1)
The writing style is clear and easy to read, but based off of the dialogue and the constant references to local lore and the connection that the villagers have, it's clear that it's a story set in a very specific place with a group of people who will be telling it for years to come.