Fluctuations within the ligand shell of a nanoparticle give rise to a significant degree of anisotropy in effective pair interactions for low grafting densities [B. Bozorgui, D. Meng, S. K. Kumar, C. Chakravarty, and A. Cacciuto, Nano Lett. 13, 2732 (2013)]. Here, we examine the corresponding fluctuation-driven anisotropy for gold nanocrystals densely passivated with short ligands. In particular, we consider gold nanocrystals capped by alkylthiols, both in vacuum and in ethane solvent at high density. As in the preceding study, we show that the anisotropy in the nanoparticle pair potential can be quantified by an angle-dependent correction term to the isotropic potential of mean force (PMF). We find that the anisotropy of the ligand shells is distance dependent, and strongly influenced by ligand interdigitation effects as well as expulsion of ligand chains from the interparticle region at short distances. Such fluctuation-driven anisotropy can be significant for alkylthiol-coated gold nanoparticles, specially for longer chain lengths, under good solvent conditions. The consequences of such anisotropy for self-assembly, specially as a function of grafting density, solvent quality and at interfaces, should provide some interesting insights in future work. Our results clearly show that an isotropic two-body PMF cannot adequately describe the thermodynamics and assembly behavior of nanoparticles in this dense grafting regime and inclusion of anisotropic effects, as well as possibly many-body interactions, is necessary. Extensions of this approach to other passivated nanoparticle systems and implications for self-assembly are considered.