They do in fact have nothing to do with each other. Inverse-square is a simple conservation-of-energy argument for point sources, i.e. it basically assumes that no absorption takes place anywhere – which is a pretty good approximation for dry air, provided of course there are no solid obstacles anywhere.
Stokes' law is much more specific in that it starts with a plane wave, while inverse-square amounts to a spherical-wave model. Now, any wave looks locally like a plane wave if you zoom in close enough, but Stokes' law only makes sense if you look at an area much larger than the wavelength. Which you can do with a spherical wave, but you need to move out far away from the source, where $r^2$ becomes basically constant1.
For audio applications, Stokes' law is largely irrelevant, because a) you'll hardly get to a proper plane-wave scenario and b) the viscosity of air is so low that the predicted absorption is usually much smaller than any losses at solid boundaries, and to the inverse-square spreading. Where Stokes' law is important is at high frequencies in fluids with significant viscosity, e.g. in medical ultrasonic scans.
Inverse-square itself needs to be handled with care: in lots of applications, reflection plays a significant role, so the spreading is limited and the intensity drops slower than $1/r^2$, or there are solid obstacles between source and observer so the intensity is obviously lower.
1For the purpose of its effect on magnitude only. Of course, the variations in $r$ still act on the phase, where a large offset doesn't play any role.