That contends that he is a Kenyan citizen, hence a British Subject. We did not have dual citizenship with Great Britian in 1961, so he did not qualify at birth to be a US Citizen.
That doesn't make sense. Obama's mother, so far as I can tell lived all her life prior to her 14th birthday in the US.
If you're talking about the former rule that the US citizen parent had to have lived in the US for 10 years, five of them after the age of 14 for children to be citizens, that applied to children born outside of the US. If Obama was born in the US to a US parent he was a US citizen from birth.
To say that we didn't have or recognize dual citizenship with Great Britain, means that we didn't recognize that American citizens could also have British citizenship. It doesn't mean that those who could possibly claim foreign citizenship weren't American citizens. It means that Britain's claim was irrelevant so far as requirements for US citizenship are concerned.
But she left the United States with Obama in Kenya, and that is where she got pregnant, then came back to the US, so she did leave the US, which started the clock all over, and was not back in the US 5 years before the birth.
Its US law.