This paper investigates the dynamic control of non-reciprocal propagation for vortex beams in a Rydberg atomic ensemble mediated by flying spin atomic clusters. The system comprises a target Rydberg atomic ensemble with a five-level \calN -type structure and two flying spin atomic clusters moving at velocity v, coupled through position-dependent non-resonant dipole-exchange interactions to form a hybrid quantum system exhibiting dipole-exchange-induced transparency. The macroscopic relative motion between the flying spin clusters and the stationary target ensemble induces optical non-reciprocity. Using the split-step Fourier propagation method combined with the superatom model, we perform numerical simulations to analyze the spatial evolution of a probe Laguerre-Gaussian (LG) vortex beam. To quantify nonreciprocity, we introduce the LG nonreciprocity index CLG, defined through the difference in normalized mean absolute intensity between output spots for left and right incidences. Our findings show that the spin cluster velocity v and the probe detuning (\varDelta_\mathrmp ) are key parameters governing the non-reciprocal response. By adjusting v and \varDelta_\mathrmp , we can flexibly manipulate both the intensity and phase profile of the transmitted two-dimensional vortex wavefront. In the presence of dipole-exchange interaction, the output spot undergoes marked stretching deformation, deviating from an ideal annular shape, and its stretching direction (e.g., along x or y axis) can be precisely switched through parameter adjustment. Moreover, the input direction of the probe beam influences the output phase pattern, producing counterclockwise phase rotation for left incidence and clockwise rotation for right incidence. This work reveals a dynamic control mechanism for non-reciprocal propagation of structured light through macroscopic motion of spin clusters and underscores the potential of dipole-exchange-induced transparent systems for designing nonreciprocal optical devices. These results lay a theoretical foundation for optical information processing and quantum communication, and suggest a viable technique for two-dimensional vortex beam shaping with broad application prospects.