We use molecular dynamics and transition-matrix Monte Carlo simulation to study the ability of entropy scaling relationships to describe kinetic properties of the extended simple point charge water model. We examine translational and rotational diffusivities, a characteristic relaxation time for rotational motion, and a collective relaxation time stemming from analysis of the coherent intermediate scattering function. We consider both the thermodynamic excess entropy and the contribution to the two-body excess entropy related to center-of-mass correlations as scaling variables. Calculations are performed over a broad range of conditions that span from the dense supercooled liquid regime to the critical region. We find that the thermodynamic excess entropy serves as a suitable metric for describing reduced transport properties for state conditions corresponding to temperatures above the onset of water's structurally anomalous region, defined by states points for which the excess entropy increases upon compression at constant temperature. In contrast, the aforementioned two-body contribution to the excess entropy cannot be used to quantitatively predict kinetic properties over the wide range of conditions explored here. For state points above the onset temperature of the structurally anomalous region, reduced transport property data collapse onto common curves when expressed as a function of the thermodynamic excess entropy. Below this temperature, data fall onto isochore-specific curves. Our results show a relatively strong correlation between the translational diffusivity and excess entropy and a noticeably weaker correlation between rotational mobility and excess entropy.