An air conditioner is a heat pump. It uses energy to pump heat from one end to another. One of these thermoelectric generator devices is basically the reverse, it generates energy when heat is pumped through it. There is perhaps an analogy here to a water pump, pumping water from one place to another, and a water wheel, generating energy when water is pumped through it.
Take an ordinary house. The default, low-energy state is the one it tends to if we don't mess with it. The inside and outside of the house come to about the same temperature as energy leaks in through the insulation and holes in it, though slowly.
Now we put in a heat pump. This changes the system. With a little energy input, we capture the energy in the inside of the house, and we move it to the outside. The energy state of the system changes, it begins to gain energy as we put some in to create the heat differential.
Then we attempt to capture this heat differential. We place a heat engine, which one of these devices is, across our temperature differential. Assuming total efficiency for both processes, which we do not in reality have, our heat engine undoes the heat differential and produces for us the exact amount of energy we ourselves put in to create that heat differential. The inside and outside now come to some resting state, possibly with a constant heat differential upheld by the pump and actively sabotaged by the engine. Theoretically, we get net 0 energy and dysfunctional air conditioning, but in practice, we get a net loss of energy to inefficiencies.
The same applies to the water analogy. Imagine two tanks of water connected by a porous wall. The state it reaches naturally is that both tanks are at the same level through water seepage, though it is slow. If we place in a pump, we get a pressure differential across the tanks: one tank becomes higher and another lower. Then we place a wheel across the differential to take advantage of that pressure. Energy is generated, and at the same time the height difference is lost. Again net 0, though in reality you will experience a lot of inefficiencies.
If the point is to do air conditioning, you cannot recapture energy from the heat. Just running the air conditioner at a lower power achieves the same result more efficiently. Similarly with the water pump, it will in reality be more efficient to just not pump as much water up, and you will reach the same result.
Not really : Peltier-based devices like this add (some) resistance to the heat flow. This added resistance means the air conditioner (or any heat pump, e.g. a fridge) gets less efficient.
I think the energy captured by the device will always be lower than the extra energy needed for the heat pump.
A device like this is not useful in a system where you are actively pumping heat around.
