Macromolecular diffusion in dense colloidal suspensions is an intriguing topic of interdisciplinary relevance in Science and Engineering. While significant efforts have been undertaken to establish the impact of crowding on the dynamics of macromolecules, less clear is the role played by long-range ordering. In this work, we perform Dynamic Monte Carlo simulations to assess the importance of ordered crowding on the diffusion of globular macromolecules, here modelled as spherical tracers, in suspensions of colloidal cuboids. We first investigate the diffusion of such guest tracers in very weakly ordered host phases of cuboids and, by increasing density above the isotropic-to-nematic phase boundary, study the influence of long-range orientational ordering imposed by the occurrence of liquid-crystalline phases. To this end, we analyse a spectrum of dynamical properties that clarify the existence of slow and fast tracers and the extent of deviations from Gaussian behaviour. Our results unveil the existence of randomly oriented clusters of cuboids that display a relatively large size in dense isotropic phases, but are basically absent in the nematic phase. We believe that these clusters are responsible for a pronounced non-Gaussian dynamics that is much weaker in the nematic phase, where orientational ordering smooths out such structural heterogeneities.