No, this is a mischaracterization of what Wolfram is saying. Wolfram says: why consider computer programs to be valuable as mere
approximations to the underlying analytic models, when you can consider computer programs
themselves to be an entirely new and unexplored land of complex and interesting models.
Traditional computer science considers computer programs to be merely a means to an end.
A quite delicious irony is given by the example of Naiver Stokes equations. They are themselves an idealization of the flow of fluids composed of discrete particles. Because of our obsession with continuous models, we mostly resort to laboriously solving them numerically -- but it turns out that simple lattice gas cellular automaton models are actually 1) fairly accurate 2) much more computationally efficient, and 3) more suggestive of the underlying microscale physics.
To step back a bit, a helpful analogy would be that simple computations are the 21st century equivalent of differential equations, which were studied rigorously in their own right starting in the 18th century, often prior to their application to concrete problems.
Whether this intuition will turn out to be prescient, or whether it will fizzle out, is another question.