From the article:
“...According to the Kenya Citzenship and Immigration Act, a person born outside Kenya shall be a citizen by birth if on the date of birth that person’s mother or father was or is a citizen by birth. ...”
In 1961, Kenya was a colony of Britain.
O Sr had British citizenship so any children born to him while Kenya was a British colony would be British.
Feel free to read all the comments in that post.