We investigate the electronic structure of silver nanowires at 1 monolayer (ML) Ag coverage on a vicinal Si(557) substrate by angle-resolved photoemission spectroscopy. Fermi surface mapping reveals two-dimensional (2D) Ag-induced electron pockets, which shift to higher binding energies by n-type doping of the step edges. The electronic structure of the 1 ML Ag/Si(557) system exhibits additional 2D metallic states near the Fermi level, which may originate from substrate induced periodicities. By considering the confining potential and electronic coherence length we reconcile the seemingly conflicting views of the dimensionality in this system probed by photoemission spectroscopy, and the dispersion of collective excitations as detected by electron energy loss spectroscopy.