The 22nd Amendment was proposed (and passed) by Congress in 1947, and ratified by the states in 1951. Without that "shall not apply" language, Truman (the President when the 22nd was proposed) would have been barred from running again.
Further evidence of that being the line of thinking is the second part of that sentence; the allowance of one who would suddenly be violating the Constitution upon ratification to finish serving the term. Never mind that Truman was previously exempted, or that thanks to the timing and the presence of the 7-year time limit, it could not have been used by anyone else.
Photo op, the tall skinny Kerry, arm sort of raised...hand in hand with the not so tall and slim Hill.
Picture the Shot from behind as they wave to the thundering herd at the convention.
Caption
kerry describes her as "our tremendous asset...".
In the corner
Der Shlickmeister: "I do not have sex with that woman".