Well, the figure in the reference you provided is quite simplistic, so you should take care when trying to reproduce results. For example, there is no indication of how the device should be separated into electrodes and a quantum transport region. The VNL device configuration is therefore not supposed to look exactly like the illustration!
If you for example want to reproduce the bandstructure calculations in Fig 2, you would indeed set up a device configuration just like the one you already made. Remember how a device is defined: a finite transport region (finite along the transport direction) sandwiched between two infinite leads (considered infinite, or bulk-like, along the transport region). It therefore makes no sense to have a gate or dielectric in the electrode regions (indeed, this is simply not possible in VNL), because gates and dielectrics are by definition part of the quantum transport region.