  Recently there has been a great interest in understanding quantum spin liquid
phases with varying spin magnitude, partly due to possible material
realizations. A number of recent numerical computations suggest that the ground
state of the S=1 Kitaev model may be a quantum spin liquid in analogy to the
renowned $S$=$1/2$ model. On the other hand, the nature of the ground state
remains elusive since the $S$=$1$ model is not exactly solvable in contrast to
the $S$=$1/2$ model. In this work, we construct a tensor network ground state
wavefunction for the S=1 Kitaev model, which is explicitly written in terms of
physical spin operators. We explain how this class of wavefunctions can be
successfully used for variational computations and compare the outcomes to
known results on finite size systems. We establish the existence of distinct
topological sectors on torus by constructing the minimally entangled states in
the degenerate ground state manifold and evaluating topological entanglement
entropy. Our results suggest that the ground state of the S=1 Kitaev model is a
gapped quantum spin liquid with Z2 gauge structure and Abelian quasiparticles.
