The link given in the post above (post 121 I think) says that a child born out of wedlock in a foreign country to a US citizen mother who had been in the US for a year is an American citizen at birth.
They key words are ‘out of wedlock’.
Stanley Ann was married to Barrak Sr.
IF, IF, he was born in Kenya the marriage was valid, so Barrak, Jr. is a Kenyan both by location of birth, and father’s citizenship.
If he was born in Hawai’i, then the marriage was not valid (bigamy), and he is an American, both by location of birth, and his mother’s citizenship.
That makes seeing his REAL birth certificate crucial to knowing his eligibility.