It looks like it is still a Republic even though it doesn't have Republic in the text of the Constitution.
Our form of government is also a Republic, but the word doesn't occur in our Constitution either, only the word Republican.
“The United States shall guarantee to every State in this Union a Republican Form of Government”
Since the Kenya Constitution in 1963 looks like it was a Republic, (as is the USA, even if the word is not in our Constitution) it doesn't really prove whether they were using the word Republic of Kenya or not earlier than the change in the text of their Constitution. But it's good to have the original text.