You're right, it's a stylised version of what they did when they were kittens - some cats even drool at the same time. I suppose it feels good in the same way that we like hugs because they remind us of being hugged when we were small. There's a strange parent/child relationship with cats - they enjoy being treated like kittens (eg this padding movement of their paws, and being stroked is like being washed by their mother) but at the same time they try and teach us how to hunt by bringing in half-alive creatures.