No way it can work. Peltier cells are relatively inefficient heat pumps, that is, they move heat from say side A to side B, and lose some power into heat, so they need a big heatsink and possibly associated fan on side B to get to interesting low temperatures on side A. That little box shown in the photo will never work unless they give it a way to expel the heat in excess in a way that doesn't affect who is wearing them ("Hey, that thing lowered my underpants temperature by 10 degrees C; too bad it also released 20 degrees C hotter air in my shirt!" - numbers pulled from you-know-where, just to illustrate the point).

That inefficiency also creates one more problem: assuming they solve the getting-rid-of-hot-air one, this thing will work as an heater for the room in which it works, because some power is always lost into heat, which will turn in less efficiency for the heat pump since it is now working in a hotter environment. And there's power consumption too: peltier devices of decent size draw amperes, not milliamperes, so a pocket sized device like that one, assuming they can change the laws of physics and solve all other problems, won't offer any benefit for more than maybe a couple hours at half power.

My conclusion is that toy is no more than a marketing gimmick that will never work, but (thanks to Sony's name too) as with all non working gimmicks that rely on 1% of correct-but-not-usable-here science and 99% of marketing, it will be cloned and produced in quantities by far east companies to be sold for cheap online, only to be immediately thrown away in some landfill.