High-resolution particle image velocimetry (PIV) particle-to-velocity analyses using small interrogation areas (IAs) often require substantial processing time. To overcome this limitation, a generative adversarial network (GAN)-based model is proposed to achieve spatio-temporal super-resolution (SR) reconstruction from low-resolution PIV data with large IAs, thereby significantly reducing post-processing time. Time-resolved PIV measurements of plasma-induced vortex flows, covering vortex formation, growth, transition and breakdown stages, are employed to train and evaluate the model with multi-scale vortical structures. By sequentially constructing spatial and temporal datasets, the GAN-based model enables reliable SR reconstruction at different scaling factors. Reconstruction accuracy is systematically assessed using time-averaged, instantaneous and phase-averaged velocity fields. At SR factors of $\times$4 and $\times$8, the reconstructed fields closely match high-resolution references, effectively capturing both fluctuating velocities and small-scale vortical structures. In contrast, $\times$16 reconstructions exhibit diminished accuracy due to the loss of fine-scale information from highly downsampled inputs. For time-averaged fields, high-resolution reconstructions reliably capture plasma jet characteristics at all SR factors. To enhance generalisation, transfer learning is introduced to fine tune the parameters of SR-related layers in the generator, enabling accurate reconstructions under varying vortex dynamics. In addition, the efficiency gains in PIV particle-to-velocity analysis and the fundamental limitations on achievable SR factors imposed by spatio-temporal data correlations are discussed. This study demonstrates that GAN-based spatio-temporal SR models offer a promising approach to accelerate PIV analyses while maintaining high reconstruction fidelity with diverse flow conditions.