In modern Internet of electric energy, i.e., networked power systems, data-driven schemes based on advanced machine learning methods have shown high potential in system emergency stability control, e.g., undervoltage load shedding (UVLS) against the short-term voltage stability (SVS) problem. However, how to efficiently and adaptively select the most effective UVLS sites for online SVS enhancement is still a challenging task. Faced with this issue, this article develops an intelligent short-term voltage trajectory sensitivity index (VTSI) prediction scheme for adaptive UVLS site selection. Specifically, the scheme is realized by designing a powerful structure-aware recurrent learning machine (SRLM), which systematically combines the emerging graph convolutional network (GCN) with the recurrent long short-term memory algorithm. By doing so, the SRLM is not only fully aware of the non-Euclidean structure of the power grid but also capable of amply capturing temporal features during SVS dynamics. Consequently, it manages to implement efficient and precise VTSI prediction, thereby reliably identifying critical UVLS sites in various scenarios. Numerical case studies on the Nordic test system illustrate the efficacy of the proposed scheme.