In the field of skeleton-based human action recognition, Graph Convolutional Networks (GCNs) have become a dominant framework. However, existing GCN-based approaches often treat the sequences of two-person interaction as separate entities, ignoring the inherent semantic dependencies and spatial correlations between interacting subjects. Furthermore, high-order skeleton representations naturally exhibit non-Euclidean structures, where Euclidean deep learning models are inherently limited in explicitly capturing and preserving such geometric information. As a countermeasure, we propose a Riemannian Graph Convolutional Network (RGCN) that operates on the Symmetric Positive Definite (SPD) manifolds. Specifically, we model high-order skeletal statistics via Gaussian embedding and propose a Riemannian network to capture inter-subject interactions and global correlations. The proposed RGCN is instantiated under three SPD geometries, and its effectiveness is validated through extensive experiments on three interaction benchmarks. Extensive experimental results show that RGCN provides a competitive and geometrically grounded alternative for skeleton-based interaction recognition.