It doesn't connect to your phone, it just authenticates via the app. I deal with a company where people use thin clients that run WhatsApp on the remote desktop. It's not an unusual case.

Interesting, I apparently skimmed the "Link to your phone" section too quickly (and I guess have a different sense of what that phrase implies than the author of that README, since a "link" that no longer requires the other end to exist anymore doesn't really seem like a link at all).