That's like the wild Cottontails in our yard at feeding time. Young bunnies play just like kittens.
They do. In fact, we have two rabbits right now, and I had cats when I was in high school, and I can say that rabbits have a lot of personality similarities with cats. The biggest difference in personality I've noticed is that rabbits tend to like snuggling for a much longer time than cats do (which is a plus in my book).