I'm sorry, Kevin. My sympathies to you and your family.
Like blunted, neni and chomps said, an animal is never "just" an anything. They become part of us. They are souls in bodies different than ours. But they experience love and joy and emotion just like we do. Except they are the masters of it.
I think that's part of the hurt from the loss, feeling like that connection to such pureness is gone. But we're always connected to them through our hearts and memories.
Looks like he lived like a king indeed. What a bright and engaging character in the videos! I knew he'd use that hanging block toy as an escape ladder ha. You are all lucky to have shared your lives together.