Physical-Layer Authentication (PLA) offers endogenous security, lightweight implementation, and high reliability, making it a promising complement to upper-layer security methods in Edge Intelligence (EI)-empowered Industrial Internet of Things (IIoT). However, state-of-the-art Channel State Information (CSI)-based PLA schemes face challenges in recognizing mobile multi-users due to the limited reliability of CSI fingerprints in low Signal-to-Noise Ratio (SNR) environments and the constantly shifting CSI distributions with user movements. To address these issues, we propose a Temporal Dynamic Graph Convolutional Network (TDGCN)-based PLA scheme. This scheme harnesses Intelligent Reflecting Surfaces (IRSs) to refine CSI fingerprint precision and employs Graph Neural Networks (GNNs) to capture the spatio-temporal dynamics induced by user movements and IRS deployments. Specifically, we partition hierarchical CSI fingerprints into multivariate time series and utilize dynamic GNNs to capture their associations. Additionally, Temporal Convolutional Networks (TCNs) handle temporal dependencies within each CSI fingerprint dimension. Dynamic Graph Isomorphism Networks (GINs) and cascade node clustering pooling further enable efficient information aggregation and reduced computational complexity. Simulations demonstrate the proposed scheme's superior authentication accuracy compared to seven baseline schemes.