> the dogs were not killed but were buried there before their master died
Sure. There is still a massive difference between a burial for a King having someone or something buried with them and conducting the ritual entirely for a pet. (And looping back to OP, several cultures conducted funeral rites entirely for beloved pets. The Egyptians and Romans come to mind.)
Forgive my ignorance, but is the difference because a burial FOR a dog implies some meaningful significance since the focus is on the pet, whereas being buried WITH the dogs is just a way for the dogs to be sent to the afterlife with the deceased (and the focus isn't on them, they're just along for the ride)?
Yes. The one is focused on the pet, elevating it to the same level of respect and dignity as funeral rites for people.
The other is not - it could be respectful (I loved my pet please bury them by me) or not (bury my jewels and slaves with me) but it still isn't the raising of the pet status to that of your own species.
Sure. There is still a massive difference between a burial for a King having someone or something buried with them and conducting the ritual entirely for a pet. (And looping back to OP, several cultures conducted funeral rites entirely for beloved pets. The Egyptians and Romans come to mind.)