Short gamma-ray bursts (SGRBs) are produced by the coalescence of compact binary systems which are remnants of massive stars. GRB 160410A is classified as a short-duration GRB with extended emission and is currently the farthest SGRB with a redshift determined from an afterglow spectrum and also one of the brightest SGRBs to date. The fast reaction to the Neil Gehrels Swift Observatory alert allowed us to obtain a spectrum of the afterglow using the X-shooter spectrograph at the Very Large Telescope (VLT). The spectrum shows several absorption features at a redshift of z = 1.7177, in addition, we detect two intervening systems at z = 1.581 and z = 1.444. The spectrum shows Ly alpha in absorption with a column density of log (N(H i)/cm(2)) = 21.2 +/- 0.2 which, together with Fe ii, C ii, Si ii, Al ii, and O i, allow us to perform the first study of chemical abundances in a SGRB host galaxy. We determine a metallicity of [X/H] = -2.3 +/- 0.2 for Fe ii and -2.5 +/- 0.2 for Si ii and no dust depletion. We also find no evidence for extinction in the afterglow spectral energy distribution modelling. The environment has a low degree of ionization and the C iv and Si iv lines are completely absent. We do not detect an underlying host galaxy down to deep limits. Additionally, we compare GRB 160410A to GRB 201221D, another high-z short GRB that shows absorption lines at z = 1.045 and an underlying massive host galaxy.