[tiagoespinha]

Your phone connects to WhatsApp's servers. So does your laptop. The bridging is likely done server-side. I assume this is done because WhatsApp is (probably) using end-to-end encryption, so everything must be ran by your phone (which is the only place where your private key is stored) in order to encrypt the messages.

[JosephRedfern]

It works impressively well, though -- I use it far more than I do the mobile client directly.