It says that, but the flow inside the can will be three-dimensional and not well modeled by the Rankine vortex. And no, the Rankine velocity profile is nowhere zero.

This gadget exploits a common technique for enhancing heat transfer; another example are pipes designed to transport fluid while also causing it to come to thermal equilibrium with the environment as quickly as possible: these pipes sometimes feature rifling which spins the fluid as it flows through them.

If this doesn't lead to carbonation explosions it's because the spinning is not very fast and doesn't lead to much shear.

In short, this is very well understood, in fact utterly routine, technology.

EDIT: On second thought the combined canned fluid + bath fluid together might roughly be considered Rankine-like; this might be what they mean. In that case the fluid inside the can would be in (very roughly) solid-body motion, which implies little agitation (shear).