Does the Hadith "Part of honoring the dead is burying them" include animals, given that the questioner buried his animal based on this Hadith?

First: "The honoring of the dead is in their burial" is not a Prophetic Hadith (definition), but rather a saying of some jurists, and its meaning is sound.

Second: It is not said concerning an animal when it dies, "Its honor is in its burial," as is said concerning a human. Nevertheless, it is legislated to bury an animal if doing so prevents harm to Muslims, such as removing a nuisance or a foul smell from their path. The Prophet, peace and blessings be upon him, encouraged benefiting from the hide of a dead sheep and did not command its burial. Furthermore, the burial of insects, beasts, and the like is a broad matter, and it is preferable to bury them so that no one is harmed by them.