I would like to once again stress, as done maybe 20 times, when asked here on the Forum that the kind of plot shown there is NOT supported in ATK yet (we're planning to add it in version 2016). The plot indicates the contribution of a particular subset of atoms or orbitals to the total band structure. What is implemented in ATK, using the projection list, is the "projected band structure" for a certain subset of atoms or orbitals, which has DIFFERENT eigenvalues compared to the total band structure. Thus, that data cannot be used to draw the plot as shown, which I would call a "contribution-resolved band structure" (although the terms projected band structure is not inappropriate, it's just that we use it for something else already).
The purposes are simply different: the projected band structure can be computed for a surface with a molecule attached, or an interface between two materials, and compared to the corresponding "simple" band structure of the clean surface or bulk material. Then, the projected band structure shows how much the band structure is modified. Another typical use for this is to project out the bulk states, and only look at the surface states, by projecting on the surface atoms.
This can still be relevant in your system: you can compute the band structure of "graphdiyne in the presence of Ag(111)", and compare it to the clean graphdiyne bands. But it will not give the plot you show.
