Is there any specific rule that requires someone supervising and awarding a Ph.D. to have a Ph.D. themselves? I learned recently in some parts of Asia it is possible to have a Masters degree and award a Ph.D. One point made was, in the example of Korea, there was no education system and as such it was required for this to be the case at some point. This seems to have continued. Does this exist in United States or Europe as well?
No, there isn't any general rule.
First, a PhD degree is awarded by a university, not by an individual.
The education system of a country or the university rules usually define which positions can officially act as supervisors. The same education system or the university rules establish which titles should have a person to be eligible for those positions: if the PhD is not required, which is not uncommon, there can certainly be PhD supervisors without a PhD.
Another case is the following: in Italy the PhD degree has been established some thirty-odd years ago. This means that most of those who became professors in Italy before that time don't have a PhD (as Federico rightly observes, some might have taken it abroad), but they surely can supervise students officially.