TL;DR: it's just using the WiFi networks' names to decide whether you're close or not.

I thought "environmental fingerprints" were referring to something more elaborate, like a fingerprint of the local audio environment, or using the accelerometer to measure the local spacetime curvature.

It's not limited to WiFi networks and indeed the fingerprints you suggest would be a lot better because they would change significantly over time. The whole WiFi networks idea kinda stuck because it's an obvious an easy thing to grab from the environment using a mobile phone. An audio fingerprint would definitely be doable on mobile.