3DSystems is one of the biggest players in 3D printing. PolyJet, VFlash and ZCorp are both theirs, and they even have Botmill and RapMap.
They're now starting their own Shapeways-style "cloud printing" service called Cubify, and are offering a consumer 3D printer "Cube" which is effectively an FDM printer not unlike the RepRap.
The parts shown off in the video are actually not made using the Cube but were printed with Cubify, it looks like they were made by a high-end SLA machine.
It will be interesting to see if they can compete with Shapeways and if the Cube will be good for puzzles.
The Cube is extremely similar to the Up! 3D printer, which seems to me like one of the best consumer solutions out there. It simply uses the same material for build as for support and you can easily snap the supports away. There are two major obstacles: resolution and material cost.
Dimenson's FDM cartridges are extremely expensive (say, 50% of the total Shapeways cost) but it would be possible to offer them much cheaper and I hope they do. If the resolution is good enough then combined with some solvent smoothing you could make really good puzzles with this that look and feel very close to actual mass produced ones.
I've heard the printer itself will be $1300, which is nothing compared to my annual Shapeways budget