The paper studies the processes of Penning ionization (PI) involving Rydberg states of alkali atoms in cold gas media. Within the binary model framework, PI analysis has been performed in terms of the autoionization widths of a quasi-molecule formed by an atomic pair of collision partners. The obtained data on the PI cross-sections σ_ revealed interesting and structurally diverse features of σ_i behavior depending on the quantum numbers of the Rydberg states of the atomic pair subjected to a long-range dipole-dipole interaction. In contrast to previous works, which focused mainly on the hydrogen atoms case, a strong instability of σ_i with respect to the variations of orbital quantum numbers was observed.