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Investigations into the magnetic properties of sputtered Mn$_{x}$CoGe films in the range $0.8 \leq x \leq 2.5$ uncovered ferrimagnetic order, unlike the ferromagnetic order reported in bulk samples. These films formed hexagonal Ni$_{2}$In-type structures when annealed at temperatures below 600$^{\circ}$C. While the Curie temperatures of the films are comparable to those of hexagonal bulk MnCoGe, there is a reduction in the magnetization of the Mn$_{x}$CoGe films relative to bulk MnCoGe, and a magnetization compensation point is observed in the $x<1$ samples. To understand the behavior, we calculated the magnetic moments of Mn-antisite defects in MnCoGe with density-function theory (DFT) calculations. Models constructed from the calculation suggest that films become ferrimagnetic due to the presence of Mn on the Co and Ge sites. In the $x<1$ samples, these defects arose from the disorder in the films, whereas for $x>1$, the excess Mn was driven onto the antisites. Mean field modeling of the temperature dependence of the magnetization provides additional evidence for ferrimagnetism. Our mean field and DFT models provide a description of how the variation in film defects with composition will transition the magnetic behavior from a compensated (V-type) to an uncompensated (Q-type) ferrimagnet.