  We prove that the enumerative polynomials of quasi-Stirling permutations of
multisets with respect to the statistics of plateaux, descents and ascents are
partial $\gamma$-positive, thereby confirming a recent conjecture posed by Lin,
Ma and Zhang. This is accomplished by proving the partial $\gamma$-positivity
of the enumerative polynomials of certain ordered labeled trees, which are in
bijection with quasi-Stirling permutations of multisets. As an application, we
provide an alternative proof of the partial $\gamma$-positivity of the
enumerative polynomials on Stirling permutations of multisets.
