If they are using a conventional Peltier, then it is correct that you would need a 120W or so device to cool an 80W processor. To keep it at 26° C you would need to keep the hot side of the Peltier at around 50° C. The Peltier would be drawing about 110 to 120 watts(the wattage rating of a Peltier is the maximum heat that it can pump at zero temperature differential, not the power that it uses). This would give a total heat load approaching 200 watts. Assume that the environment in the PC case is 40°C maximum. This means the heat sink must dissipate 200 watts with a temperature rise of 10°C, which is a thermal resistance of 0.05°C/W. Clearly the little heat sink/fan in the picture is not up to this task. You would need one of the following:
1)a liquid heat sink
2)a bonded fin heat sink about 5"x5"x4" high plus a 120 mm fan
3)an 8" x 12"x2" high extrusion plus a 160mm fan
The small heat sink in the picture will at best offer a thermal resistance of around 0.25°C/W.
Therefore, we are definitely not dealing with a conventional Peltier. Since the device is "electronic", it is not a compressor, either.
It is possible that they have a much more efficient Peltier(current devices operate at less than 10% of the maximum possible efficiency, termed the Carnot efficiency). At the Carnot efficiency, you only need 6.5 watts to keep an 80 watt microprocessor at 26°C(assuming the heat sink is at 50°C). Let's say a device exists that operates at half the Carnot efficiency. You then have only 93 watts total that you need to get rid of, and suddenly that small heat sinkmight be up to the task if you can keep the air in the case under 30°C. That's certainly an easier job when you have less total heat to get rid of.
If they have indeed invented a much more efficient Peltier(or similar cooling device), then they are the world's biggest fools choosing this as it's first application. At best, CPU cooling is a niche application for Peltiers. The real money would be in conventional refrigeration, and a device this efficient(and noiseless to boot) would obsolete compressor-based refrigeration in short order. It could literally make someone a trillionaire since it can also also be used to efficiently generate electricity from low-level heat sources like geothermal heat, thus making fossil fuels and nuclear fission obsolete. In short, it could change our world for the better very quickly, and I'm sure anyone smart enough to invent an improved Peltier would be smart enough to see it's potential. Therefore, I highly doubt that it's an improved Peltier. Either that, or my opinion of marketing departments just went even lower than even I thought possible(all those idiotic auto commercials are mainly responsible for my low opinion of marketing "professionals").
What is it? I haven't a clue, but if it's hyped as much as the Segway, we're in for a big disappointment.