We present Spitzer 24 mu m imaging of 1.5 < z < 2.5 distant red galaxies (DRGs) in the 10' x 10' extended Hubble Deep Field-South of the Multiwavelength Survey by Yale-Chile. We detect 65% of the DRGs with K-AB < 23.2 mag at S-24 mu m >= 40 mu Jy and conclude that the bulk of the DRG population is dusty active galaxies. A mid-infrared (MIR) color analysis with IRAC data suggests that the MIR fluxes are not dominated by buried AGNs, and we interpret the high detection rate as evidence for a high average star formation rate of < SFR > = 130 +/- 30 M-circle dot yr(-1). From this, we infer that DRGs are important contributors to the cosmic star formation rate density at z similar to 2, at a level of similar to 0.02 M-circle dot yr(-1) Mpc(-3) to our completeness limit of K-AB = 22.9 mag.