Dice Become Ordered When Stirred, Not Shaken
More accurately, cubes pack more closely when agitated one way than another.  The fact that they are dice is irrelevant (they don't become ordered with respect to the facing side).  To be honest, this isn't particularly odd, as the experiment removed the component of the agitation that would tend to displace the cubes vertically, which is the only dimension with an asymmetric force that would tend to increase the packing factor if undisturbed (gravity).