Well, it could be a story about a lost alebrije. Maybe it got separated from its kind during a great storm. The short story would detail its attempts to find its way back home. Along the way, it meets various other creatures, both friendly and not so friendly, and has to use its wits and unique alebrije abilities to overcome obstacles.
An alebrije short story could be about the magical and colorful alebrijes. It might tell of their origin in Mexican folklore, how they are fantastical creatures that are a blend of different animals. For example, it could describe an adventure of a boy who stumbles upon the world of alebrijes and befriends one, learning about their unique powers and the significance they hold in the cultural imagination.