Doesn't that use the whatsapp web api? Which requires you to have Whatsapp installed on your phone as it routes all communication to the phone where it is decrypted?
And yeah, it's be forwarded and re-sent through the phone/VM. But this is the best trade-off I've found for dealing with people that refuse to leave WhatsApp. I look accommodating and don't just cut out someone I presumably need to care about, but also limit how much data FB gets.
And while I haven't tested this, I'm now curious how always having WhatsApp Web active affects my "Last Seen" time...