The origin of higher-order exchange interactions in localized S-state systems has been the subject of intensive investigations in the past. In particular, it has been suggested that a biquadratic exchange term may arise from the magnetoelastic energy. Here we report on the pressure and temperature dependence of the excitation spectra of magnetic Mn2+ dimers in CsMn0.28Mg0.72Br3 probed by inelastic neutron scattering. Biquadratic exchange and a strong distance dependence of the bilinear exchange are observed. It is shown that the mechanism of local exchange striction may explain the occurrence of biquadratic exchange in accordance with the elastic properties of the compound.