Does the world exist for the NPC's?
Yes, or at least, they can.
The proof of this is that things can happen and events can progress "off stage". And in particular, many GM's feel some obligation to have the events that transpire off stage be believable, so that if the PC's were there, they would observe something that could happen within their frame of reference. Thus the events that occur on and off stage are operating by the same set of rules.
Now, a much tougher to answer question is, "Ought the world exist for the NPCs?"
There are certainly times even in a world where events occur offstage, where in the best interests of the story the GM freezes events until the PC's arrive. That is, you can have events which are triggered in the metagame by the PC's arrival which couldn't be plausibly triggered in world by the PC's arrival. In other words, you can have coincidences in your game world that the PC's are a part of, and most of the time the players will wave suspension of disbelief regarding those sort of events because they are a common element of all sorts of narrative fiction.
Yet events like that suggest the world doesn't exist until the PC's arrive.
For my part, I mix and match. There are times I run a game as if the world of the NPCs is fully alive and advancing without the PCs as if the world of the NPCs was being simulated, and I also have coincidences where events happen when the PC's arrive at a location.
One thing that is true of any table top RPG, is that the world of the NPCs is never as fully simulated as the world of the PC's. A human moderator has many advantages over a computer, but the ability to simulate everything is not one of them.