With the widespread use of renewable energy sources (RES) in the smart grid, the next generation power system, short-term load forecasting (STLF) is of critical importance in grid stability and energy optimization. Traditional STLF models include issues such as high computational cost, dependency on cloud infrastructure, and latency issues, which are undesirable for real-time energy management. To solve these issues, the EdgeAI paradigm, which combines edge computing and artificial intelligence (AI), can be a promising solution. EdgeAI reduces the dependency on cloud-based systems by processing data close to the data source, offering advantages such as low latency and low bandwidth. Thus, it increases the response speed by processing data in real time, making it suitable for STLF applications. In order to benefit from all these advantages, the EdgeAI-driven Hybrid Echo State Network and Gated Recurrent Unit (ESN-GRU) model is introduced for real-time and efficient STLF in this paper. ESN-GRU combines the fast training capabilities of ESN and sequential learning capabilities of GRU, and offers the advantages of high prediction performance and low latency inference in STLF. Experimental results show that the proposed model improves the R2 score by 2.5% and significantly reduces the MAPE value from 129 to 0.101 compared to existing models. Benchmark results in edge environment prove that ESN-GRU provides up to 79% and 92% faster inference compared to state-of-the-art methods.