We design a gesture-recognition pipeline for networks of distributed, resource constrained devices utilising Einsum Networks. Einsum Networks are probabilistic circuits that feature a tractable inference, explainability, and energy efficiency. The system is validated in a scenario of low-power, body-worn, passive Radio Frequency Identification-based gesture recognition. Each constrained device includes task-specific processing units responsible for Received Signal Strength (RSS) and phase processing or Angle of Arrival (AoA) estimation, along with feature extraction, as well as dedicated Einsum hardware that processes the extracted features. The output of all constrained devices is then fused in a decision aggregation module to predict gestures. Experimental results demonstrate that the method outperforms the benchmark models.