That applies to births to Kenyan citzens outside the country after 1963. I haven't a clue what the law is for a 1961 birth, though it's not really much of an issue.
That would apply to anyone holding dual citizenship. Per an earlier section in Chapter 6, that would include Obama.
"Every person who, having been born outside Kenya. is on llth December, 1963 a citizen of the United Kingdom and Colonies or a British protected person shall. if his father becomes. or would but for his death have become, a citizen of Kenya by virtue of subsection (1). become a citizen of Kenya on 12th December. 1963."