Jesus that's so repressive. And I'm sure the laws are pretty subjective as well or at least not something the average chat admin is fully up to speed with. Essentially the outcome of this will be to kill chats or send it underground to tor or something.
Well, then, owners, admins and mods just need to be anonymous and untraceable. Users too, of course. So yeah, Tor or something stronger :)
For the smaller casual "circle of acquaintances (relatives, friends, coworkers, gaming teammates, etc)" chats, there should be no owner, though - small non-public invite-only communities work perfectly well without administration. This doesn't solve "poster is responsible" but it solves "owner is responsible".
For larger or open chats - yes, the owner should be someone pseudonymous (or just a robot).