I think this is still unknown. But I don't know all the content of Overlord in detail.
References have been made that, for example, Ains, and the rest of either NPCs, or potentially other players, where transported to a "new world".
But, as far as I know, it's unknown if he has been transported to a "real world" where he and all characters have now a physical body that matches the one they had in the game, or if what Ains, and any other possible player that was trapped in the world, perceive is just a extremely accurate virtual simulation.
I know that, at this point of the story, his real physical body would be long dead under normal circumstances, but I think things like that all his mind was copied while he was sleeping when the game server closed, and then transferred to some computer, or that he was kidnapped and now his body is in a Matrix-like state somewhere don't contradict anything that is on the story.
Is there any hint or evidence on which type of world the story is really happening?