Existing Artificial Intelligence (AI) approaches for compressing three-dimensional (3-D) point clouds for real-time immersion over communication networks are commonly based on energy-intensive AI architectures, e.g., transformer and autoencoder architectures. We design and evaluate the first 3-D point cloud compression based on the energy-efficient Spiking Neural Network (SNN) architecture. We conduct this evaluation within our framework of AI-based semantic compression for networked eXtended Reality (AIcXR+). We first design a goal-oriented autoencoder, wherein an Artificial Neural Network (ANN) encodes a 3-D point cloud into a compact Vector Code (VC) at the sender, and a Convolutional Neural Network (CNN) decodes the VC into volumetric pixels (voxels) for rendering at the receiver. We jointly train the ANN encoder and CNN decoder to map 3-D point cloud frames into VCs that compactly represent the volumetric semantics of the 3-D point clouds. Then, we convert this trained ANN/CNN into an SNN, bypassing the standard backpropagation training of SNNs. For robotic surgery datasets, we evaluate the SNN relative to the ANN/CNN as well as a (non-AI-based) semantic color-coding approach (cXR+). We find that both SNN- and ANN-AIcXR+ achieve approximately the same compression ratios as cXR+, while achieving substantially shorter computing (encoding + decoding) latencies than cXR+; thus, AIcXR+ substantially reduces the aggregate (computing + communication network transmission) latency compared to the non-AI-based cXR+. Importantly, we find that the SNN reduces the energy consumption by nearly an order of magnitude compared to the ANN while achieving essentially the same reconstruction quality.