Human activity recognition (HAR) with millimeter-wave (mmWave) radar offers a privacy-preserving and robust alternative to camera- and wearable-based approaches. In this work, we propose the Occupancy-Gated Parallel-CNN Bi-LSTM (OG-PCL) network to process sparse 3D radar point clouds produced by mmWave sensing. Designed for lightweight deployment, the parameter size of the proposed OG-PCL is only 0.83M and achieves 91.75 accuracy on the RadHAR dataset, outperforming those existing baselines such as 2D CNN, PointNet, and 3D CNN methods. We validate the advantages of the tri-view parallel structure in preserving spatial information across three dimensions while maintaining efficiency through ablation studies. We further introduce the Occupancy-Gated Convolution (OGConv) block and demonstrate the necessity of its occupancy compensation mechanism for handling sparse point clouds. The proposed OG-PCL thus offers a compact yet accurate framework for real-time radar-based HAR on lightweight platforms.