Transition metal oxides are of interest as cathodes for rechargeable, non-aqueous Mg²⁺ batteries due to the possibility for high voltage and capacity when paired with a magnesium metal anode. In general, it has been found that Mg²⁺ storage in oxides is much more sluggish than monovalent cation storage such as Li⁺ or H⁺. Several strategies have been proposed to overcome the kinetic activation barrier of Mg²⁺ storage in oxides, including the use of interlayer structural water and nanostructuring. While hydrated metal oxides such as MnO₂ and V₂O₅ have been investigated, relatively little is known about the exact role of the structural water in such materials during Mg²⁺ storage. In this study, we utilize a model system of crystalline tungsten oxides with different degrees of hydration (WO₃·nH₂O, where n = 0, 1, or 2). This materials system allows for an investigation of two different types of structural water: one that is covalently bound to tungsten, and one that is present only in the interlayer. The effect of covalently bound water has not yet been investigated for Mg²⁺ storage. Using cyclic voltammetry and ex situ Raman spectroscopy and scanning electron microscopy, we find that in these materials, the Mg²⁺ energy storage mechanism is due to intercalation. Moreover, we find that the interlayer water in WO₃·2H₂O is not stable in a non-aqueous electrolyte and that the material quickly transforms to WO₃·H₂O. However, the covalently bound water in WO₃·H₂O is stable and as a result, this material exhibits faster kinetics than WO₃. The improved kinetics come at the expense of the capacity, which decreases by approximately half as compared to the anhydrous material. These results provide additional insights into the benefits and drawbacks to use of hydrated metal oxides for Mg²⁺ storage.