Depth (or lack of depth) is part of the aesthetic.

That flat design is aesthetically different does not necessarily mean you no longer have an information hierarchy, or that it doesn't direct your eye, or that it does not entice user actions. It simply has different methods of accomplishing these tasks.

Since all of these tasks come through the visual approach and execution of the design, I'd say that falls well in line with the definition of "aesthetics."

[edited for spelling and style]