Domain Generalization (DG) has been recently explored to enhance the generalizability of Point Cloud Classification (PCC) models toward unseen domains. Prior works are based on convolutional networks, Transformer or Mamba architectures, either suffering from limited receptive fields or high computational cost, or insufficient long-range dependency modeling. RWKV, as an emerging architecture, possesses superior linear complexity, global receptive fields, and long-range dependency. In this paper, we present the first work that studies the generalizability of RWKV models in DG PCC. We find that directly applying RWKV to DG PCC encounters two significant challenges: RWKV's fixed direction token shift methods, like Q-Shift, introduce spatial distortions when applied to unstructured point clouds, weakening local geometric modeling and reducing robustness. In addition, the Bi-WKV attention in RWKV amplifies slight cross-domain differences in $key$ distributions through exponential weighting, leading to attention shifts and degraded generalization. To this end, we propose PointDGRWKV, the first RWKV-based framework tailored for DG PCC. It introduces two key modules to enhance spatial modeling and cross-domain robustness, while maintaining RWKV's linear efficiency. In particular, we present Adaptive Geometric Token Shift to model local neighborhood structures to improve geometric context awareness. In addition, Cross-Domain $key$ feature Distribution Alignment is designed to mitigate attention drift by aligning $key$ feature distributions across domains. Extensive experiments on multiple benchmarks demonstrate that PointDGRWKV achieves state-of-the-art performance on DG PCC.