Gait is a behavioral biometric modality that can be used to recognize individuals by the way they walk from a far distance. Most existing gait recognition approaches rely on either silhouettes or skeletons, while their joint use is underexplored. Features from silhouettes and skeletons can provide complementary information for more robust recognition against appearance changes or pose estimation errors. To exploit the benefits of both silhouette and skeleton features, we propose a new gait recognition network, referred to as the GaitPoint+. Our approach models skeleton key points as a 3D point cloud, and employs a computational complexity-conscious 3D point processing approach to extract skeleton features, which are then combined with silhouette features for improved accuracy. Since silhouette- or CNN-based methods already require considerable amount of computational resources, it is preferable that the key point learning module is faster and more lightweight. We present a detailed analysis of the utilization of every human key point after the use of traditional max-pooling, and show that while elbow and ankle points are used most commonly, many useful points are discarded by max-pooling. Thus, we present a method to recycle some of the discarded points by a Recycling Max-Pooling module, during processing of skeleton point clouds, and achieve further performance improvement. We provide a comprehensive set of experimental results showing that (i) incorporating skeleton features obtained by a point-based 3D point cloud processing approach boosts the performance of three different state-of-the-art silhouette- and CNN-based baselines; (ii) recycling the discarded points increases the accuracy further. Ablation studies are also provided to show the effectiveness and contribution of different components of our approach.