The recent emergence of ubiquitous, multi-platform eye tracking has raised user privacy concerns over re-identification across platforms, where a person is re-identified across multiple eye tracking-enabled platforms using personally identifying information that is implicitly expressed through their eye movement. We present an empirical investigation quantifying a modern eye movement biometric model's ability to link subject identities across three different eye tracking devices using eye movement signals from each device. We show that a state-of-the art eye movement biometrics model demonstrates above-chance levels of biometric performance (34.99% equal error rate, 15% rank-1 identification rate) when linking user identities across one pair of devices, but not for the other. Considering these findings, we also discuss the impact that eye tracking signal quality has on the model's ability to meaningfully associate a subject's identity between two substantially different eye tracking devices. Our investigation advances a fundamental understanding of the privacy risks for identity linkage across platforms by employing both quantitative and qualitative measures of biometric performance, including a visualization of the model's ability to distinguish genuine and imposter authentication attempts across platforms.