An inelastic neutron scattering study of the spin waves corresponding to the stripe antiferromagnetic order in insulating Rb$_{0.8}$Fe$_{1.5}$S$_2$ throughout the Brillouin zone is reported. The spin wave spectra are well described by a Heisenberg Hamiltonian with anisotropic in-plane exchange interactions. Integrating the ordered moment and the spin fluctuations results in a total moment squared of $27.6pm4.2mu_B^2$/Fe, consistent with $mathrm{S approx 2}$. Unlike $X$Fe$_2$As$_2$ ($X=$ Ca, Sr, and Ba), where the itinerant electrons have a significant contribution, our data suggest that this stripe antiferromagnetically ordered phase in Rb$_{0.8}$Fe$_{1.5}$S$_2$ is a Mott-like insulator with fully localized $3d$ electrons and a high-spin ground state configuration. Nevertheless, the anisotropic exchange couplings appear to be universal in the stripe phase of Fe pnictides and chalcogenides.
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