According to some legal theories. But, IMHO, if he was a natural born citizen, and never renounced it himself as a legal adult, then he *is* a natural born US Citizen, regardless of the fact that other nations may have or may still claim him as one of theirs. It's US laws and its Constitution that count, not those of other nations.
So yes, it's still possible that he renounced it at some point, possibly by traveling on a passport from Indonesia or even Kenya, but it's a long shot.
What is the year of the regs you listed?? Berg based his analysis on the regs effective in the 1960’s. Hawaii will accept registration of births by Hawaiian residents whose child is born overseas. That is why seeing the info on the birth certificate is important to confirm the place of birth. If both of BO parents were US adult citizens, BO is an American born citizen. However BO mother is American but under 21 thus not an adult and his father is over 21 thus a Kenyan adult. Under the laws of that time BO can take on the nationality of the adult in the relationship (father). This is what I mean by the intricacies of the laws that govern status of US born and how one can lose it. Berg is using US laws of the 1960’s as the basis to determine BO’s nationality requirements. I think what you listed applies to contemporary law and if both parents are Americans and over 21 years of age.