The theory of the kinetic exchange in a pair of orbitally degenerate ions developed by the authors [J. Phys. Chem. A 102, 200 (1998)] is applied to the case of face-shared bioctahedral dimer (overall D-3h-symmetry). The effective kinetic exchange Hamiltonian is found for a T-2(2)-T-2(2) system taking into account all relevant transfer pathways and charge-transfer crystal field states. The influence of different transfer integrals involved in the kinetic exchange on the energy pattern and magnetic properties of the system is examined. The role of other related interactions (trigonal crystal field, spin-orbit coupling) is also discussed in detail. Using the pseudoangular momentum representation and the technique of the irreducible tensor operators of R-3-group we give a general outlook on the nontrivial symmetry properties of the effective Hamiltonian for the D-3h-pair, and on the magnetic anisotropy arising from the orbital interactions specific for the case of orbital degeneracy. The magnetic properties of the binuclear unit [Ti2Cl9](-3) in Cs3Ti2Cl9 are discussed with a special emphasis on the magnetic anisotropy experimentally observed in this system. The existing exchange models for [Ti2Cl9](-3) and the concept of the effective Hamiltonian are discussed in the context of the present study.