If you watch that video closely you'll see that it's not the quad faces that become hexagons, but the quad corners which form the center of the hexagons.
so. here's my take:
create your quad "box". select ALL the verts and add these to a new set.
Triangulate the mesh (regular triangulation, not add divisions)
Mesh Smooth (defaults as before)
select the vertices in the set - convert selection to EDGES - Delete edge/vertex
you now have your base hex mesh. I'm not sure exactly how you'd emulate MAX's "classic" smoothing in Maya which would be the next step, but you could use extrude face (keep faces together: OFF) on all the hexagons before deleting them as a starting point...
hope this is of some use...
:nathaN