The emotional response of robotics is crucial for promoting the socially intelligent level of human-robot interaction (HRI). The development of machine learning has extensively stimulated research on emotional recognition for robots. Our research focuses on emotional gaits, a type of simple modality that stores a series of joint coordinates and is easy for humanoid robots to execute. However, a limited amount of research investigates emotional HRI systems based on gaits, indicating an existing gap in human emotion gait recognition and robotic emotional gait response. To address this challenge, we propose a Gait-to-Gait Emotional HRI system, emphasizing the development of an innovative emotion classification model. In our system, the humanoid robot NAO can recognize emotions from human gaits through our Trajectories-Aware and Skeleton-Graph-Aware Spatial-Temporal Transformer (TS-ST) and respond with pre-set emotional gaits that reflect the same emotion as the human presented. Our TS-ST outperforms the current state-of-the-art human-gait emotion recognition model applied to robots on the Emotion-Gait dataset.