Abstract We present optical observations of the Swift short-duration gamma-ray burst (GRB) GRB 161104A and its host galaxy at z  = 0.793 ± 0.003. We model the multiband photometry and spectroscopy with the stellar population inference code Prospector and explore the posterior using nested sampling. We find a mass-weighted age of t m  = 2.12 +0.23 −0.21 Gyr, stellar mass of , metallicity of , dust extinction of A V  = 0.08 +0.08 −0.05 , and low star formation rate of 9.9 × 10 −2 M ⊙ yr −1 . These properties, along with a prominent 4000 Å break and optical absorption lines, classify this host as an early-type, quiescent galaxy. Using Dark Energy Survey galaxy catalogs, we demonstrate that the host of GRB 161104A resides on the outskirts of a galaxy cluster at z  ≈ 0.8, situated ≈1 Mpc from the likely brightest cluster galaxy. We also present new modeling for 20 additional short GRB hosts (≈33% of which are early-type galaxies), finding population medians of and t m  = 1.07 +1.98 −0.67 Gyr (68% confidence). We further find that the host of GRB 161104A is more distant, less massive, and younger than the four other short GRB hosts known to be associated with galaxy clusters. Cluster short GRBs have faint afterglows, in the lower ≈11% (≈30%) of observed X-ray (optical) luminosities. We place a lower limit on the fraction of short GRBs in galaxy clusters versus those in the field of ≈5%–13%, consistent with the fraction of stellar mass of ≈10%–20% in galaxy clusters at redshifts 0.1 ≤  z  ≤ 0.8. Future studies that take advantage of wider-field and deeper cluster surveys are needed to understand the true rate of short GRBs in clusters and their effect on heavy-element enrichment in the intracluster medium.