Here we go, they contradict themselves later: "Computational general equilibrium (CGE) models provide an example of accepted computerized problem solving in economics."
I don't see this as a contradiction. The authors probably would include simulation and computerized solvers as "computerized problem solving". Such applied techniques are certainly welcomed in the field of economics. That said, they are not usually considered a theoretical approach. So, using them in a paper won't get you published if a journal is looking for a theoretical advance.
Here's my take: the paper would say that solving the AD-AD model with a computational technique with specific choices for parameters would not be considered a theoretical contribution.
I think that is an accurate characterization of economics, based on my experience of what 'theoretical' means. Why? When you use a numerical technique (i.e. not a symbolic manipulation) with particular values for the parameters, few would call that theoretical work. They'll call it applied economics.
(Side note: I can't speak from experience if the AD-AS model is usually solved with dynamic programming.)
There's a distinction between numerical approximation and simulation. The former is a technique to solve an analytical model of the world. The latter would have an analytical model of the simulation outcomes rather than of the world directly.