You don't have to guess, it says it is a thermoelectric module right on their website.
This device will work, but it is a very minimal effect. You can do the same thing with anything hot or cold. Madoka's idea of a piece of metal will do the same minimal effect, although metal might look ugly and / or have sharp corners and won't work to cool you if the metal is above body temperature (such as if it was stored outside or in a hot car).
I just use a cold pack in the freezer wrapped in a flour sack towel: it cools far more and lasts far longer than this device. Tie the cold pack onto your wrist and you are done. It isn't as elegant of a look, but I don't care for my uses.
The bigger problems that I have is that the Embr Wave can only cool for 2 minutes before needing to turn off for a long period of time. They didn't design a way to get the heat out of the device efficiently, so it would overheat if you had it on longer. And can only run 40 to 100 minutes on a charge with a brand new battery (meaning after a year or two think less than half an hour of usage per charge).