Online action detection and anticipation aim to understand current or upcoming actions in video streams. In industry, current artificial neural network (ANN)-based methods suffer from prohibitive energy consumption, fundamentally limiting their deployment on resource-constrained industrial devices. To bridge the gap between theory and application practice of informatics in industrial environments, we propose a novel knowledge distillation-based spiking neural network (KDSNN), which synergistically integrates bioinspired spike-driven processing with knowledge distillation, significantly reducing the energy consumption. Specifically, KDSNN includes a pioneering spiking neural network (SNN) architecture for online action detection and anticipation, which combines well-designed hierarchical spike convolutional neural network (CNN) block and spike Transformer block to capture spike-driven information. To further improve the performance of our SNN while maintaining low energy consumption, we introduce the knowledge distillation paradigm, which aims to utilize an expert-level ANN as a teacher to guide our SNN. Based on this, we propose a novel distillation loss, which consists of feature distillation and logit distillation. Notably, to address the cross-domain feature alignment in feature distillation, the optimal transport theory is employed to realize cross-domain knowledge transfer for the first time by minimizing the Wasserstein distance between continuous features (ANNs) and discrete features (SNNs). Through extensive evaluations on THUMOS14 and EPIC-Kitchen-100 datasets, the energy consumption of our KDSNN is only 27.1% and 10.0% of the state-of-the-art ANN-based method MAT. Equally importantly, the parameter count of our KDSNN is only 37.0% and 27.7% of MAT on THUMOS14 and EPIC-Kitchen-100, respectively.