The rovibrational structure of the He2Cl2 van der Waals cluster in the X and B electronic states is studied by means of full dimensional quantum-mechanical calculations. He2Cl2 is the smallest cluster containing helium for which rotationally state-resolved data are available and for which the effects of Bose statistics are important. The He2Cl2 wave functions exhibit quite large amplitude motions, particularly for the He-He bending mode [associated with the angle formed between the two He-(center of mass of Cl-2) bonds]. The preferred geometry of the ground van der Waals state is planar, with the He-He axis perpendicular to the Cl-2 axis. It is shown that a reduced dimension model for the He-He bending vibration together with a rigid structural model reproduces well the low-lying energy levels of the complex and allows us to assign proper statistical weights to the asymmetric top transitions of the B <--X spectra. In particular, the symmetry under He exchange of the rigid rotor levels is shown to depend on the He-He bending level. The observed excitation spectra are successfully simulated using the proposed model. The effective rigid structure that best reproduces the rotationally excited levels with a rigid rotor analysis is a distorted tetrahedron where the He-He angle is approximately 130 degrees. This difference from the 180 degrees most probable configuration is due to the complex dependence of the moments of inertia on the internal degrees of freedom for such a floppy molecule. Therefore, structural information obtained from observed spectra of this or similar clusters should be carefully analyzed to avoid reaching misleading conclusions. Fragmentation rates for He2Cl2(B,upsilon =10-13) are, for the first time, extracted from experimental data, confirming that the dissociation process is mainly sequential.