As far as I can cell the bonding energy is computed for just the left electrode with the nanocone attached, calculated as a slab geometry. This is quite reasonable, I don't think it would be beneficial to compute the bonding energy in a device geometry.
You can do the same calculation in ATK (the authors appear to have used VASP for this), however one should note that to get a really accurate result you need to account for the basis set superposition error (BSSE). This is somewhat complicated, but we are working on an easier approach for ATK 13.8.