Describe how the properties of water allow cats to drink in this fashion, including how water's molecular structure contribute to this process

The way a cat drinks liquid is credited to the two forces that they have to balance: inertia and gravity. The cat doesn't dip its tongue to the liquid. It just merely touches the surface. As it touches the surface, there is an adhesive force that attracts the water molecules to the surface of the tongue of the cat. The cat then brings it back in a fast pace taking advantage of the inertia before gravity overcomes and the water drops back to the bowl. So, the contribution of the water molecules are in the adhesive force. The rest is the work of the cat's motion.

Yes it would be a physical change.