Inelastic neutron scattering is employed to study the reciprocal-space structure and dispersion of magnetic excitations in the normal and superconducting states of single-crystalline Rb0.8Fe1.6Se2. We show that the recently discovered magnetic resonant mode in this compound has a quasi-two-dimensional character, similar to overdoped iron-pnictide superconductors. Moreover, it has a rich in-plane structure that is dominated by four elliptical peaks, symmetrically surrounding the Brillouin zone corner, without root 5 x root 5 reconstruction. We also present evidence for the dispersion of the resonance peak, as its position in momentum space depends on energy. Comparison of our findings with the results of band structure calculations leads to a robust bulk-sensitive estimate of the electron count in the superconducting phase and provides strong support for the itinerant origin of the observed signal. It can be traced back to the nesting of electronlike Fermi pockets in the doped metallic phase of the sample in the absence of iron-vacancy ordering.