The Philosopher's Stone transfixes magical fairy tale storytelling elements within a less fairy tale-esque framing, ignoring or escaping different generic conventions in order to reconfigure what it means to be a fairy tale by taking certain literary, artistic licenses. The framework of the story with the Tristan and Isolde allusion and the embedded narratives of multiple plots within the same literary space differs from the traditional backdrop/lead-up to the fairy tale, at some points specifying a distinct moment in time and at others abstracting this conception of time and space.
At each moment independent of others, The Philosopher's Stone acquires the same thematic concerns and basic plot as the fairy tale. King Mark gets tricked. King Mark transforms. King Mark enters a robber's den. King Mark transforms. These are all things we've seen before - trickery, loss, transformation, helper/"fairy godparent" - in places we've seen before - castle, robber's den, peasant life (particularly once expelled from courtly setting). Yet this is intercut with less traditional motifs - greed, at least in the stories we've read, isn't a prominent theme... it's often featured but not the main event; adultery; gender swaps (Floribell is female); ethical decisions and lessons (the final one), often present in parables; dream sequences while still a donkey.
I could go on and on with this weird back and forth interplay between "Fairy Tale normative" and "Fairy Tale transgressive". Essentially the story uses the traditional, magical elements of the fairy tale to provide the reader with something that is easily understood and taken as normal, in order to present themes and ideas that are not part of the fairy tale world, and in fact, are extremely satiric and rational. In other words, the fairy tale tropes are only used to provide more cutting commentary on contemporary societal issues.