No its not. It is a world following Demon's Souls basically, then it's somehow resurrected by fire and constantly fights itself with these new elements. All returns to stone in the end, it's an engaging tale just in a different way than say Lord Of The Rings.
I am aware it handles fog differently but come on now. It's clear they used the bad ending of demons souls as a general outline to build from. These games are all high concept moreso than objective.
Depressing and horrors are the surface level aspects of this dark fantasy, but the game has such a bright soul compared to any other game out there. The monstrosities aspect comes from DS3 making the world grosser off the heels of Bloodborne horror development. There is an elegance to disturbing ideas that Demon's Souls and DS1 that no other game had. Maybe Sekiro and bloodborne too.
Look at this and tell me it's not related, same universe or not it's no coincidence dark souls follows with a beginning of a mysterious world shrouded in fog, however now the fog is the line between existence and non-existence. Humanity is doomed here. They are reborn from the souls. Just my theory though.
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Instead of fog closing off part of the world you play in, now it's the first flame's intense effect on Lordran that separates it from the outside world.