Okay, first of all – you have to scan the QR-Code with the scanner that is built in WhatsApp. Not with some 3rd-party scanner-app. Click on “Whatsapp Web”, then the scanner opens immediately.
BUT – apparently there is a problem with devices that have a display smaller than 4 inches!
Like with my Sony Xperia Go (3,5 inches), I can’t tap on the “OK, got it”-button to make the instructions of the built-in-scanner go away.
That’s it. They will have to solve this problem in a later version, I guess.