What's the backstory behind those "ghostly" looking animals at Mogg Latan's shrine?

These are Blupees (the small rabbit creatures), and the Lord of the Mountain (technically, a horse), aka. Satori.

Given the Hyrule Compendium description and the name of the mountain ("Satori"), they seem to be a tribute to the late Satoru Iwata -- "A sage that perished long ago".