I wasn't able to win with this one, but you might want to give the logarithmic flappy 2048 a try. It's the only one I'm able to do absurdly well on: http://logarithmic-flappy-2048.ajf.me/
edit: I did a 3d victory in the 18 minutes in editing the comment. You can generally just push higher numbers into a corner, and pick either the left or the right side to consistently fold to and you'll get it mostly without thinking.
I find 4D much, much easier to control and visualize than 3D. Maybe if 3D was somehow presented in three dimensions I'd have an easier time of it, but the 4D one was easier to grok.
That probably says something about how humans relate to interfaces that map higher dimensions to 2D planes, or maybe it's just the way the 4D layout maps to the screen.
ignore the "3d" idea. Just look at the rules of the game and play by that.
I'm sure some people can maintain clear mental models of higher order dimensions and seamlessly translate the grids on the screen in some hyperspace in the mind.
But I, my friend, have no chance of that. The more I ignore that notion, the easier it becomes.
This is the first 2048 variant that I'm able to beat. yay me... .__.