Well you own nothing except numbers on the screen, and your ownership is defined by some points in a plane that is unique and immutable, as defined by the specifications set by Satoshi and other developers themselves. I will not call this "fake rich," as those sitting in piles of numbers on their bank accounts from derivatives also lie within the same principle. Instead, I'll consider them as rich people, like the normal ones who own lots of money from successful businesses since they own something that is highly-valued by other people.

Our perception of value is something complex, and we just magically agree that something is valuable, or has value, like fiat money. If that is the case, then bitcoin is, and will be, valuable too, and if someone owns a lot of it, they are 'rich' because our perception of value says so.