Since most sensor data depend on each other, time-series anomaly detection is one of practical applications of IoT devices. Such tasks are handled by Recurrent Neural Networks (RNNs) with a feedback structure, such as Long Short Term Memory. However, their learning phase based on Stochastic Gradient Descent (SGD) is computationally expensive for such edge devices. This issue is addressed by executing their learning on high-performance server machines, but it introduces a communication overhead and additional power consumption. On the other hand, Recursive Least-Squares Echo State Network (RLSESN) is a simple RNN that can be trained at low cost using the least-squares method rather than SGD. In this paper, we propose its area-efficient hardware implementation for edge devices and adapt it to human activity anomaly detection as an example of interdependent time-series sensor data. The model is implemented in Verilog HDL, synthesized with a 45nm process technology, and evaluated in terms of the anomaly capability, hardware amount, and performance. The evaluation results demonstrate that the RLS-ESN core with a feedback structure is more robust to hyper parameters than an existing Online Sequential Extreme Learning Machine (OS-ELM) core. It consumes only 1.25 times larger hardware amount and 1.11 times longer latency than the existing OS-ELM core.