What is the "curse of dimensionality" in molecular dynamics?
It's certainly more of a "back of the envelope" calculation than a rigorous proof. The main point is, that for a certain system, the cost of obtaining a set of trajectories with a given statistical accuracy is fixed with ab initio MD, as only the dynamically relevant parts of the PES are calculated. 

With what is here called "classical MD" (but also applies to "quantum dynamics" and "wave packet" methods), the whole PES is computed in advance, and this cost is system dependent (scales with $3N - 6$ for nonlinear systems); the individual trajectories over this PES are then calculated comparably quickly.

The ratio of the two scalings is $\frac{10^{3N-6}}{10^{M+n}}$, increasing with system size (making ab initio MD favourable) and decreasing with required statistical accuracy (making classical MD favourable).