I'm pretty sure the main purpose of the 6x4 grid is for general purpose horizontal and vertical alignment, especially for images symmetric about the horizontal or vertical centre.

While we're often told to get away from putting a major feature precisely in the centre of the frame (and the 3x3 or a golden ratio helps to guide this), there are many times where it's aesthetically or technically useful to put a point/line exactly in the middle of the frame.

Note the comparison here:

Black lines are 3x3 — Dashed grey lines are 6x4 — Blue lines are rule-of-thirds (not an option).
Diagonals shown also, but I believe they're only available in Live View.

The 6x4 set of lines marks both the centre-point and the vertical & horizontal mid-points of the frame, which the other line options do not. I suspect this is the reason for adding these lines in. You could kind of line things up with the old 5D AF sensor markings (9-point and 11-point AF systems have at least 3 points along the horizontal or vertical centre-lines for alignment), but there's no such obvious markings with the 61-point AF in the 5D Mark III.

Perhaps they could have just used the centre-lines, instead of 6x4, or added some less obvious markers on the edge/centre of the viewfinder, but it seems an obvious extension to make a reasonably regular grid for general purpose alignment. That and the fact that the 6x4 grid is square, which to me suggests alignment more than anything else.

I guess it could also be useful for making square crops (from the central 4x4 grid).