The obvious answer is that the kitten is playing. We know that cat play is based on hunting but I think the answer to this question is bit more complicated that we think. In addition to cats pushing small objects around on flat surfaces they also throw balls into the air and then pounce on them. Another classic situation is a small object, say a pen, being pushed off a desk or table onto the floor and watched by the cat. That is all he does, push it off and watch it fall.
Catherine Davidson in her book Why Does My Cat Do That? says that kittens who throw a ball into the air over their heads and then pounce on it, are doing what a wild cat does in the wild when fishing. Many wild cats do eat fish and some will be successful in scooping a fish out of a pool with a paw. The fish is thrown onto dry land and then pounced on and killed. I see the similarity. Therefore, this may be a correct assessment. Although, I don’t think this form of domestic behavior is so particularly connected to one aspect of wild cat behavior.
Kittens and cats also push balls and other small objects around. They often end up under furniture. And sometimes the kitten just watches the ball move. It seems that the ball is a disappointment as it does not do enough. If you move furniture after about 6 months you’ll see a pile of small objects underneath. Pushing objects around is not replicating wild cat behavior as far as I can tell. It is more about creating the wild cat environment. It would appear to be exclusively domestic cat behavior. Something they have learned to do to try and satisfy their innermost drives and instincts.
Creating The Wild
The simple and obvious answer is that it is just play. No more and no less. It is loosely based on hunting but it is also fun. Pushing a ball over a hard surface makes it look like prey. The kitten then might chase it. It is a cat artificially creating the hunting situation. Cats live indoors, an artificial landscape in which the domestic cats inner wild traits are hard to express. He has to recreate a bit of the wild on the hoovered carpet or polished wood floor.
What about that cat who pushes a pen or any sort of small object onto the floor from a height? He’ll watch it fall, see that nothing happens when it hits the ground and then move on. He might jump down to check it out. To me this is a cat who is looking for stimulation. If there was prey in the form of a mouse he would not push pens off desks. Because there is no prey in our home (normally!) he creates it. By pushing an object off a surface it seems that he is checking if it is alive. He is hopping the object will do something when it hits the ground. He is trying to bring it to life. The human home is full of dead, inanimate objects as far as a domestic cat is concerned. Outside, in the wild, there is more life.
What about the box the cat likes to get into? This is also grounded in wild cat behavior. I sense this is the nearest thing to den that a domestic cat can get his hands on. Wild cats find somewhere safe in the day to rest up in. This is dense undergrowth or a cave or perhaps a fallen tree. That sort of place. The cat will them come out at dusk to hunt during the night. Although many wild cats also hunt during the day. In short a large cardboard box is a den and resting place.
I agree with Catherine that all these play behaviors are grounded in hunting but there are variations and sometimes the cat is recreating an artificial hunting scenario. I sense a lot of them are indicative of a bored cat. I don’t think we (me included) understand how important stimulation is for the cat. It is said that the domestic cats brain is smaller than the wild cat’s brain. They are less intelligent. This must be to do with having a soft, served-upon lifestyle without challenge. It is fortunate for us and the cat that they are also programmed to spend a lot of time sleeping. But for that the cat might have been unsuitable for domestication.