Is your question 'how does understanding the air relate to aeronautics?' The article says that they are using pollution as a way to track the trajectory of particles moving through the atmosphere. 'Air quality' is not an objective variable. Measurements of particle density are objective and there are certain mixes of these particles that are optimal for human health, but the measurements can be taken for many reasons beyond monitoring the atmosphere for unhealthy conditions (for instance, understanding how gases move through the atmosphere).

Regarding NASA, the composition of the air, and how it is changing or how it may change in the future is related to its mission in that it is scientific endeavor for the purpose of gaining knowledge and for keeping manmade objects aloft. Or maybe for making better telescopes (that see through the atmosphere). Or better communication devices. Etc.

Also, going to ignore the other bits you threw in...they have nothing to do with, well, anything