Dynamic evaluation of airport terminal capacity is critical for efficient operations, yet it remains challenging due to the complex interplay of spatial and temporal factors. Existing approaches often handle spatial connectivity and temporal fluctuations separately, limiting their predictive power under rapidly changing conditions. Here the ST-GTNet (Spatio-Temporal Graph Transformer Network) is presented, a novel deep learning model that integrates Graph Convolutional Networks (GCNs) with a Transformer architecture to simultaneously capture spatial interdependencies among airport gates and temporal patterns in operational data. To ensure interpretability and efficiency, a feature selection mechanism guided by XGBoost and SHAP (Shapley Additive Explanations) is incorporated to identify the most influential features. This unified spatio-temporal framework overcomes the limitations of conventional methods by learning spatial and temporal dynamics jointly, thereby enhancing the accuracy of dynamic capacity predictions. In a case study at a large international airport with a U-shaped corridor terminal, the ST-GTNet delivered robust and reliable capacity forecasts, validating its effectiveness in a complex real-world scenario. These findings highlight the potential of the ST-GTNet as a powerful tool for dynamic airport capacity evaluation and management.