In my understanding of the print, he said he was yes ksing, but ksing every single pokemon, which is not illegal.
The shiny KS rule applies to those that kill ONLY SHINIES, if hes ksing you normally and a shiny appear (be either normally or by shiny charm/meowth bait), we can't do anything cause that's simply Kill Stealing. But if the player either follows you/fly above you to kill SHINIES only, then yes the rule do apply.
I strongly advise you to report in game at the time of the ks, so gm's can check if the player is acting illegally or no, that print is not enough proof (specially because he admits in a certain way that he was killing every pokemon there).