What is the genre of The Lady or The Tiger?

The Lady or The Tiger can be considered an anti-fairy tale. Instead of the traditional happy ending, Stockton's short story ends on a somewhat tragic and uncertain note.
The story begins typically enough for a fairy-tale: "In the very olden time there lived a semi-barbaric king..." There is also a princess, but her character veers from archetype. This princess is beautiful; however, she is also decidedly imperious, unabashedly passionate, and violently possessive. This isn't our typically gracious, gentle, and virtuous princess of traditional lore.
Her lover is a commoner, and the intensity of their passion is clear:

This royal maiden was well satisfied with her lover, for he was handsome and brave to a degree unsurpassed in all this kingdom, and she loved him with an ardor that had enough of barbarism in it to make it exceedingly warm and strong.

Again, this isn't our typical fairy-tale, where a princess's erotic inclinations are seldom mentioned (much less alluded to). In Stockton's anti-fairy tale, the princess is both heroine and antagonist. When her lover is presented with a conundrum that threatens to either end in his death or establish him in marital bliss with a beautiful commoner, the princess's possessive nature is exposed.
The story ends on an uncertain note. Stockton doesn't reveal whether the princess's young lover is saved from the tiger or joined in holy matrimony to a beautiful maiden. What is revealed, however, is the princess's violently possessive nature. This revelation highlights the uncomfortable themes of female jealousy, gender conflict, and sociopolitical issues, all elements of the anti-fairy tale.