moving stacks in unison

To clarify, all face up cards (whether one or many) in a single pile on the tableau have to be moved in unison? (i.e. if you have a pile of 6 spades 5 diamonds 4 clubs and then you have another pile with just 6 clubs, and you need 6 spades, you cannot move the 5 diamonds 4 clubs to the 6 clubs?)

That is correct, all face up cards in a column must be moved as a unit...

I think you mean 'On the tableau' because you can't never move a pile to the foundations, right ?

That is correct..thanks for the clarification...

I checked and the official klondike rules allow for any group of cards to be moved from one column on the tableau to another. (There is no rule stating that entire columns must be moved together) Why does that rule appear here?

Check http://www.casteel.org/Pages/Klonrules.html link. It says: "According to strict Klondike rules, all the face-up cards in a column must be moved as a unit to another column".

This argument is trivial since the playing of the game doesn't change any by moving a partial stack

it does change if you have on one column (always depicted from top to bottom) 4H 3C 2D and the next 4D 3S and you have 2C on foundation.. if you move 2D to 3S, you can move 3C to foundation.. changes the game significantly..