We use hybrid molecular dynamics-multiparticle collision dynamics (MD-MPCD) simulations to investigate the influence of chain stiffness on the transport of nanoparticles (NPs) through solutions of semiflexible ring polymers. The NPs exhibit subdiffusive dynamics on short time scales before transitioning to normal diffusion at longer times. The terminal NP diffusivity decreases with increasing ring stiffness, similar to the behavior observed in solutions of semiflexible linear chains. The NP subdiffusive exponent is found to be strongly correlated with that of the polymer center of mass (COM) for the range of chain stiffnesses examined, which is at odds with the pronounced decoupling of the NP and polymer COM motions previously observed upon increasing the stiffness of linear chains. Our analysis indicates that these marked differences in the intermediate dynamics are rooted in distinct structural changes that emerge with increasing bending stiffness: Stiffer ring polymers adopt increasingly circular conformations and stack into transient tubes. The void space created near the ring centers is occupied by NPs and other polymers, resulting in strong dynamic coupling on short time scales.