Radar processing via spiking neural networks (SNNs) has recently emerged as a solution in the field of ultra-low-power wireless human-computer interaction. Compared to traditional energy- and area-hungry deep learning methods, SNNs are significantly more energy efficient and can be deployed in the growing number of compact SNN accelerator chips, making them a better solution for ubiquitous IoT applications. We propose a novel SNN strategy for radar gesture recognition, achieving more than 91% of accuracy on two different radar datasets. Our work significantly differs from previous approaches as 1) we use a novel radar-SNN training strategy, 2) we use quantized weights, enabling power-efficient implementation in real-world SNN hardware, and 3) we report the SNN energy consumption per classification, clearly demonstrating the real-world feasibility and power savings induced by SNN-based radar processing. We release evaluation code to help future research.