Kaguya as the Gedo Mazo was an outer path summoning and could rip out souls, two qualities the King of Hell has. So there is a connection between the two and are most likely from the same place of origin like Toad Summonings are. Now if you look on The King of Hell's wiki page he is based on Yama, who was part of a race called the Devas that lived in the Deva/God Realm. These Devas happened to be at war with another race known as the Asuras/Demons from the Asura/Demon realm.
I believe that Kishi is trying to do what he did with the Legend of Jiraiya and adapt the Six Realm myth into his series. As her son known the Rikudou Sennin also translates into Six Realm Sage. What do you think?