I'm skimming through the study, thanks to Sci-Hub. The researchers did account for the impact of grooming and harassement on the immune system.

We next investigated the behavioral mechanisms that give rise to social status effects on gene expression, focusing on NK and helper T cells where the observed effects were strongest. Mediation analysis revealed that rates of received harassment—a measure of the agonistic, competitive element of social status inequality— contributed to these effects for 17.3% (helper T) and 7.8% (NK) of rank-responsive genes, respectively. However, in rhesus macaques, dominance rank also influences affiliative social interactions (15). Grooming rates mediated rank effects on gene expression levels for 17.6% of genes in helper T cells, comparable to the results for agonistic interactions. In contrast, grooming behavior was more important than harassment for rankresponsive NK genes (n = 560 genes, 33.4% of all rank-responsivegenes; chi-squared test P = 1.33 × 10e−74)(Fig. 2, D and E). A lack of positive social interactions may therefore be equally or more important than social subordination per se in shaping social status effects on gene expression, consistent with the known effects of social integration on health and mortality in both humans and other primates (16–18).