  We study the spin-$S$ Kitaev model in the classical ($S \to \infty$) limit
using Monte Carlo simulations combined with semi-classical spin dynamics. We
discuss differences and similarities in the dynamical structure factors of the
spin-$1/2$ and the classical Kitaev liquids. Interestingly, the low-temperature
and low-energy spectrum of the classical model exhibits a finite energy peak,
which is the precursor of the one produced by the Majorana modes of the $S=1/2$
model. The classical peak is spectrally narrowed compared to the quantum result
and can be explained by magnon excitations within fluctuating one-dimensional
manifolds (loops). Hence the difference from the classical limit to the quantum
limit can be understood by the fractionalization of magnons propagating in
one-dimensional manifolds. Moreover, we show that the momentum space
distribution of the low-energy spectral weight of the $S=1/2$ model follows the
momentum space distribution of zero modes of the classical model.
