While the Mo$_6$S$_8$ chevrel phase is frequently used as cathode material in Mg-ion batteries, theoretical studies on this material are comparatively scarce. The particular structure of the Mo$_6$S$_8$ phase, with rather loosely connected cluster entities, points to the important role of dispersion forces in this material. However, so far this aspect has been completely neglected in the discussion of Mo$_6$S$_8$ as cathode material for mono- and multivalent-ion batteries. In this work we therefore have studied the impact of dispersion forces on stability and kinetics of Mo$_6$S$_8$ intercalation compounds. For this purpose, a series of charge carriers (Li, Na, K, Mg, Ca, Zn, Al) has been investigated. Interestingly, dispersion forces are observed to only slightly affect the lattice spacing of the chevrel phase, nevertheless having a significant impact on insertion voltage and in particular on the charge carrier mobility in the material. Moreover, upon varying the charge carriers in the chevrel phase, their diffusion barriers are observed to scale linearly with the ion size, almost independent of the charge of the considered ions. This indicates a rather unique and geometry dominated diffusion mechanism in the chevrel phase. ... mehrThe consequences of these findings for the ion mobility in the chevrel phase will be carefully discussed.