The game does need to download a model[1] to do the face tracking, and right now that does happen after you enable your webcam[2]. but once that model is downloaded the game runs fine with wifi disabled
alternatively the code is open-source (and linked on the page), so if you really wanted to you could check it out and then build it yourself: https://github.com/nolenroyalty/paccam
[2] it's a reasonable heavy download, didn't really want to put it on page load, although in retrospect it'd have given me a much more satisfactory response here!
Not use it at all. Outside of manually reviewing the code running in your browser, or a few other totally overkill measures, that’s the only real way to be certain.