Origin of the king punch
It is simply physical strength... combined with flair put in by Oda.

There are a lot of odd abilities in one piece that are not devil fruits or have any real explanation.  Sanji legs catch fire and don't burn him.  Zoro makes tornadoes. Fishmen summon water from thin air.  The king's punch is odd in our world but, there, it is just a very strong punch that takes a lot of focus, warming up, and talent to use.

There doesn't appear to be any haki, devil fruit, or weapons.