Extended Reality (XR) headsets are increasingly integrating eye tracking for enhanced user experience, adaptive interfaces, and foveated rendering. However, this rich biometric signal introduces new privacy risks. In this work, we demonstrate that eye-tracking data collected by commercial XR devices can be exploited to infer sensitive user activity. We leverage users' gaze sequences captured while interacting with a VR app to classify the type of content a user is watching. Our results reveal that eye movements alone, without any video or audio context, carry enough information to accurately predict content categories. We discuss the implications of this threat and outline how eye tracking can potentially be used to fingerprint applications and user behavior. This work is a step towards exposing and mitigating emerging privacy threats in immersive systems.