I am confused. Anyone understand this new 3-D Facebook app?

The "new" facebook 3D photos (where moving the mouse over the photo seems to move the viewpoint) is typically generated by use of a 2D image obtained by one main high-rez rear camera, and a depth map obtained by using a secondary low-rez rear camera that has a (very) small interaxial separation. Software generates the depth map (two files are generated).

There are many modern phones that have this arrangement, which is typically used to obtain a false bokeh (blurring of distant elements), as well as some other computational photography purposes.

These files are uploaded (they might be combined) and facebook performs the rest.

There are frequent artifacts generated by this technique, particularly around edges, where software has to "guess" at filling in obscurations, or other errors (such as partial pseudo stereo sections) arise.

Here's a side by side crosseye example of two views (capturing screen shots) of the extreme left and right renderings of an actual "facebook 3D photo".  While is works well, note the pseudo rendering of the closest stones at the bottom...

Note the problem pseudo at the bottom... also the background has been computationally blurred by the software.

Its obvious that with the close separation, it works best for close subjects.

Is it 3D?  Yes.

Is it "stereoscopic"? It can be, if you accept some computational errors.

There is currently a difference in meaning between "3D" and "stereoscopic".