Personally, I don't feel like the Basilisk should be considered an animal since basilisks aren't really animals. However, I don't like that they classified him as Reptile, Lizard as opposed to Animal, Lizard because lizards are reptiles and reptiles are animals. I think that's a bit silly. I also think it's a little inconsistent that the Highland Unicorn is considered an animal and not the Basilisk. But perhaps it has to do with their world lore and we just don't know it yet.