Gas kick events in drilling operations are characterized by strong coupling dynamics, subtle early-stage evolution, and severe class imbalance, which limit the effectiveness of conventional feature-independent monitoring methods. To address these challenges, this paper proposes a structure-aware intelligent monitoring framework for early gas kick detection. First, multivariate drilling parameters are modeled as an interacting graph, and a graph neural network (GNN) is introduced to capture relational dependencies and anomaly propagation behaviors at the structural level. Second, to mitigate abnormal sample scarcity and enhance temporal discriminability, a representation enhancement strategy integrating conditional tabular generative adversarial networks (CTGAN) and shapelet-based temporal patterns is developed. Finally, a multi-level interpretability mechanism combining graph attention analysis and SHAP attribution is constructed to provide transparent insights into both structural interactions and feature contributions. Experiments conducted on real drilling datasets demonstrate that the proposed GNN baseline achieves the highest accuracy (0.7302) among various machine learning and deep learning models. With representation enhancement, the GNN+CTGAN+Shapelet model further improves accuracy to 0.7507 and F1-score to 0.7347, validating the effectiveness of the enhancement strategy. Interpretability results reveal that the model decisions are primarily driven by flow-rate and standpipe-pressure-related temporal evolution patterns, which are consistent with drilling engineering knowledge. Overall, the proposed framework provides a structurally consistent, robust, and interpretable solution for intelligent gas kick monitoring in modern drilling operations.