Yes, the paper is meaningless. A very well-argued brand of meaningless-- but still. "Efficiency" of computation doesn't matter. It's also a slick glide from saying that a problem is soluble in polynomial time to saying it's easy. No. That's computer speak. Polynomial time is not defined as "easy;" it's not even necessarily fast. (It deals more with the scale-up than with the actual difficulty).
The Schrödinger equation is a differential equation-- that means, the solution at any given point in time and space depends on the fields and wave function, and the derivatives of the fields and wave function at that point-- it's local. So, the universe doesn't have to "solve" the Schrödinger equation; it only has to solve the equation for time t + epsilon, given the initial condition of the solution at time t. This is NOT a polynomial-time problem. If the universe is twice as big, it has twice as many calculations to do... and twice as much "stuff" to do it with. It's local.
The difficulty is that wave-function collapse is not local. This is inherent in the mathematical logic of quantum mechanics. It's not a matter of how hard it is to compute.