Well, you could just use the 3D widgets whenever a 3D mesh is selected or the respective 3D Move/ Rotate/ Scale tools? Perhaps a short excursion to the help files rather than just watching tutorials?
The example you linked to is not really 3D in as much as the camera/view does not move through 3D space, but the stacked individual layers are fixed in relation to each other, which makes it reasonably simply. On the other hand, you are talking about websites, and I strongly suspect there is a lot of software out there that would make this a cinch.
How about starting a parallel question in the Dreamweaver forum? It's unusual for a 'how to do it' question to go so long before the first answer in this forum, so you've got nothing to loose.
If all else fails, we can tell you how make the static 3D layers from your example video using Photoshop. It's not terribly difficult, but there are a few steps so it would take someone a bit of time.
That example has not been done in 3D.
It is taking layers and simulating 3D by transforming them and adding layer styles (e.g. shadows)
I suggest you look at Edit - Transform - Perspective, Edit-Transform-Scale and Layers Styles -drop Shadow.
The example below was done in just a few minutes using only those tools. With some more work you could make it look better