The adoption of Millimeter-Wave (mmWave) radar devices for human sensing, particularly gait recognition, has recently gathered significant attention due to their efficiency, resilience to environmental conditions, and privacy-preserving nature. In this work, we tackle the challenging problem of Open-set Gait Recognition (OSGR) from sparse mmWave radar point clouds. Unlike most existing research, which assumes a closed-set scenario, our work considers the more realistic open-set case, where unknown subjects might be present at inference time, and should be correctly recognized by the system. Point clouds are well-suited for edge computing applications with resource constraints, but are more significantly affected by noise and random fluctuations than other representations, like the more common micro-Doppler signature. This is the first work addressing open-set gait recognition with sparse point cloud data. To do so, we propose a novel neural network architecture that combines supervised classification with unsupervised reconstruction of the point clouds, creating a robust, rich, and highly regularized latent space of gait features. To detect unknown subjects at inference time, we introduce a probabilistic novelty detection algorithm that leverages the structured latent space and offers a tunable trade-off between inference speed and prediction accuracy. Along with this paper, we release mmGait10, an original human gait dataset featuring over five hours of measurements from ten subjects, under varied walking modalities. Extensive experimental results show that our solution attains 24% average F1-Score improvement over state-of-the-art methods adapted for point clouds, across multiple openness levels.