In this study, we have considered the contribution of the higher-twist (HT) effects of the subprocesses to inclusive pion pair production cross section in the high energy proton-antiproton collisions by using various pion distribution amplitudes (DAs) within the frozen coupling constant approach and compared them with the leading-twist contributions. The feature of the HT effects may help the theoretical interpretation of the future PANDA experiment. The dependencies of the HT contribution on the transverse momentum p(T), the center of mass energy root s, and the variable x(T) are discussed numerically with special emphasis put on DAs. Moreover, the obtained analytical and numerical results for the differential cross section of the pion pair production are compared with the elastic backward scattering of the pion on the proton. We show that the main contribution to the inclusive cross section comes from the HT direct production process via gluon-gluon fusion. Also, it is strongly dependent on the pion DAs, momentum cut-off parameter Delta p, and < q(T)(2)> which is the mean square of the intrinsic momentum of either initial parton.