Arikado Alucard expands on the Creature of Chaos castle thing, calling Castlevania a spiritual entity made from Dracula's magic. Which furthers the idea that Soma did in fact destroy Castlevania upon killing the Chaos spirit flowing through it, which with Dracula gone, was probably the only thing keeping Castlevania alive.
Castlevania was never destroyed by Soma defeating Chaos. To quote from DoS' library:
Dracula's Castle
The symbol of Dracula's dark power, its appearance coincides with Dracula's resurrection. The priest of the Hakuba Shrine had sealed it in a solar eclipse in 1999. Then, during the solar eclipse of 2035, it sought a new master, but failed. Now, its dark power awaits the rise of a new dark lord...
Thus, the castle still exists, albeit inside the solar eclipse. People may not like DoS for their own reasons, but it's still "canon."
About the "Death God"/Shinigami stuff:
CoD never hinted anything about it, just Zead saying "No one escapes from me." I suppose it's similar to Thanatos being the God of Death in Greek Mythology (and in God of War); they are both beings that are the representatives of death, nothing more, nothing less.