The convergence of 6G and WiFi technologies promises unprecedented online connectivity, enabling immersive experiences such as the Metaverse, with a particular emphasis on VR gaming. Despite these advancements, they bring to light considerable privacy concerns, especially the ability of adversaries to deduce personal information from encrypted gaming network traffic. Focusing on VR headsets and Nintendo Switch consoles, this study explores the privacy implications within such network environments. By simulating the typical network conditions of online multiplayer games, we expose potential privacy breaches by adversaries from both WiFi and WAN, including mobile service providers. Classical machine learning algorithms can successfully classify games and gaming consoles with an accuracy exceeding 90%, further dissecting the network traffic to unveil distinct signatures and assess privacy risks.