It seems as if "rights of personality" are a form of copyright protection. Does anyone have more insight into how this works, in Croatia or the UK? In the USA, copyright infringement would more likely be handled through the use of a DMCA complaint filed with Youtube (or whichever other media site was used). There are, however, limits to how this can be used- the Fair Use principle means that parts of his video can be used as part of a video discussing or critiquing (or, yes, criticizing) him. There is also the fact that he enjoys just this sort of protection from the WTS for his extensive use of their footage, and the fact that Youtube will punish misuse of the copyright enforcement system (ie, if you file false/frivolous DMCA claims, you risk having your channel sanctioned as a result).
Indeed, you might have expected this to be his first avenue of action if he was being maliciously defamed. For one, it's much easier and would be much more effective. But if you're wrong, or just trying to use those tools to hit back at your detractors, you might end up in a much worse spot- sanctioned for your attempts to silence them, which would lead to more videos from those same detractors. And they'd probably be even harsher than the ones he was trying to get shut down.
As for their claims of the crime of insult, that only matters if you're doing so on Croatian soil. There are some European countries that treat defamation as a criminal matter, but I don't think the UK is one of them. And the USA treats it as exclusively a civil matter. It's an empty threat, all the more so for being printed in bold and underline.
I do like the touch at the end where, after making threats and demands, they add "if You [sic] are willing to resolve this situation in an amicable manner." Again... LOL.