This is rather mysterious cat behavior. The kittens have been dumped onto a hard surface; I suspect for the purpose of making the video. They are probably looking for their mother and a warm surface. The kittens are not roughhousing in my opinion.
The father seems to think that they are playing and has joined in. He prods them as if in a play fight and then starts to ‘shadow box’. I have seen cats do this before. There is a classic case of a cat looking at boxers on television and the cat copies them. Cats ‘shadow boxing’ fascinates people and videos of it always do well.
My feeling (and I am most definitely open to correction) is that the father cat has been ‘stimulated’ into a mock play-fight by the sight of his offspring romping around together when, in fact, they are not exactly doing that. When he prods them with his paw he is engaging in play with them in a very delicate way. He is not trying to stop the kittens as has been suggested by some people. He then does the classic ‘shadow boxing’ behavior which is cat play-fighting without another cat being on the receiving end!
What do you think?