We present optical observations of the Swift short-duration gamma-ray burst (GRB) GRB 161104A and its host galaxy at $z=0.793 pm 0.003$. We model the multiband photometry and spectroscopy with the stellar population inference code Prospector, and explore the posterior using nested sampling. We find that the mass-weighted age $t_m = 2.12^{+0.23}_{-0.21}$~Gyr, stellar mass $log{(M/M_odot)} = 10.21 pm 0.04$, metallicity $log{(Z/Z_odot)} = 0.08^{+0.05}_{-0.06}$, dust extinction $A_V = 0.08^{+0.08}_{-0.05}$ mag, and the star formation rate $text{SFR} = 9.9 times 10^{-2} M_odot$~yr$^{-1}$. These properties, along with a prominent 4000 Angstrom break and optical absorption lines classify this host as an early-type, quiescent galaxy. Using Dark Energy Survey galaxy catalogues, we demonstrate that the host of GRB 161104A resides on the outskirts of a galaxy cluster at $zapprox 0.8$, situated $approx 1$ Mpc from the likely brightest cluster galaxy. We also present new modeling for 20 additional short GRB hosts ($approx33%$ of which are early-type galaxies), finding population medians of $log(M/M_odot) = 9.94^{+0.88}_{-0.98}$ 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 $approx 11%$ ($approx 30%$) 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 $approx 5-13%$, consistent with the fraction of stellar mass $approx 10-20%$ in galaxy clusters at redshifts $0.1 leq z leq 0.8$.
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