It might not be as clear-cut as that. Apparently, he was confident enough in his living a long and fruitful life that he never actually bothered to designate an official successor should anything happen to him. North Korea is technically still a republic rather than a monarchy, it's just been ruled by the same family for 70+ years because Kim Il-Sung and Kim Jong-Il were actually smart enough to have their line of succession sorted out.
I imagine it's not clear cut. But what's the likely alternative? His children are all too young, their brother is uninterested, and his aunt became estranged when her husband was executed.
It's hard to imagine a regency for child heirs in this day and age, even in North Korea. Which leaves either Kim Yo Jong taking power or the Kims being removed in favor of some party leader. And they purged anyone who might have assumed power several years ago.