No, it isn't. The whole point of Cantor's argument is that this list doesn't exist to begin with!I disagree. Personally, I've never thought of Cantor's argument in terms of squares and rectangles previously but I do find it to be a rather nice way of thinking about it. Cantor's diagonal proof is precisely proof of the fact that the rectangles never become squares. That's just a very straightforward reformulation of Cantor's point - the rectangle is as wide as N and as high as R.
The only thing that's bizarre here is that Leucippus for some reason doesn't seem to understand that showing that an assumption cannot hold is precisely what you're supposed to do in a proof by contradiction.