The challenge is that Structure is such a broad diverse topic in Engineering Science, beginning with geometric and topological physics principles.
Structural Engineering addresses design with solid-phase materials like metals, ceramics, polymers, and so on. “Structure” is of course also recognized in fluid-phase materials, for example vortices. Its standard these days to look at wing in flow as the systematic interaction of both kinds of structure, solid and fluid. AWES pressure fields are therefore “structural”, as mostly maintained by either solid barrier surfaces or kinematic moment. Electrostatic, electromagnetic, and gravitational “structure” can also figure in specific AWES functioning.
Air is just one major structural element of an AWES, if more so with inflated soft kites. Fabric, sticks, and lines are also major structural elements, as is Composite wing in respective AWES architectures. The derivative pressure field and wake “structures” only arise during use. Moving Air (Wind) by itself is not AWES structure.
My favorite solid AWES structure is Earth itself, as an anchor field medium. Vast inflated arch and dome structures can be anchored (“staked out”) by Earth, with no solid flying mass penalty. Earth is the ultimate stable scalable structure for our kites.