This thing does not ADD any energy to the atmosphere. It EXTRACTS energy from it.
You can't make something out of nothing. As a number of people have already written. It converts solar radiation (i.e. Light) into thermal energy. In a place such as Arizona - most of that solar radiation is reflected back into the atmosphere due to the coloring of the soil. Normally, this solar energy would not be absorbed.
To test, simply paint 1 square meter of your backyard black, and one square meter of your backyard white. Measure the temperature at the middle of each square, during the day and at dusk. Black wins. The black patch has just succeeded in adding more thermal energy (as opposed to adding light) to the atmosphere which takes longer to dissipate due to the increased amount of "green house" gasses.
Enter the tower, a place where we are now on a very large scale maximizing the thermal conversion of solar radiation into thermal energy (as opposed to simply reflecting back into space as solar radiation). The tower would be a very large stack in the air that would basically pump hott(er) air out of the top of it. I have not done the math but I suspect that you will find that the exit temperature of the top of the tower and the ambient atmosphere will be warmer.
It is almost required for this to be the case too. For the air to flow upwards it must be warmer OR of a higher pressure than the air below it. The exit is a little more difficult to clearly define as there are air turbines in the tower that will extract some of the energy from the air stream. There will presumably be thermal transfer from the walls of the tower to the ambient atmosphere as well. However, to keep the flow moving the air must have some velocity at the exit of the tower. The only way this will happen is by the exit air mass having a higher pressure or higher temperature. It is likely to have both because you have taken an enclosed space, taken ground level air, and moved it up 2,400 ft.
So the net is that you dump thermal energy into the atmosphere at an altitude and in a manner that is not part of the natural climate cycle. And then what happens? If you drive a single car down the road it is not an issue. If you drive millions of them you have global climate change.
Build these towers everywhere - and you've now modified the climate further in a way that contributes to our existing problem. This is basically my issue with this particular idea.