Layered rare-earth delafossites ARX2 with R=Yb(III) or Ce(III) received a lot of interest as potential hosts for a quantum spin-liquid ground state. Some systems of this family that show no long-range order down to the lowest-measured temperatures, such as NaYbO2, NaYbS2, and NaYbSe2, are presumed to be in a quantum spin-liquid state. However, other isostructural compounds are known to order antiferromagnetically at subkelvin temperatures. Among them, KCeS2 exhibits stripe-yz magnetic order in the triangular-lattice planes that sets in below 400 mK. Here we investigate the spin-wave spectrum of this ordered phase with powder inelastic neutron scattering and describe it using a model Hamiltonian obtained from first-principles calculations based on the complete |J,mJ) multiplet description of the Ce sites with an anisotropic nearest-neighbor exchange interaction. Combining the current understanding of the exchange interaction in the systems with the effects of texturing in the powder, we are able to model the inelastic neutron scattering spectrum with high fidelity.