They would have to instead tie Facebook messenger to a phone like Whatsapp does and use a web app to send messages directly from the device instead. I don't see how else it could be done and still be called end-to-end encryption.
And according to the article, this radical change is coming. Why is that so hard to believe?
Yeah, WhatsApp is e2e encrypted by default, but it also automatically backs up all your chat history encrypted using a WhatsApp-owned private key. Sure, you can opt-out of backups, but will your peers do as well? Without a clear spec, I think it's perfectly reasonable to be very skeptical of what will be the final product of this operation.
Now I know you didn't read the article. There were no promises made because this was based on conversations with employees, not a press release.
AFAIK, end to end encryption can't really support having multiple clients all using the same account. For example, WhatsApp's web interface is sort of wonky and goes via the phone, to get around the limitations, and I can't really see that being a solution here.
Of course, "end to end" encryption from a Messenger on the website is sort of meaningless anyway.
Improving your AFAIK here. Signal Desktop works independently without proxying communications through the phone (which is what WhatsApp does). Wire supports multiple platforms (Windows, Mac, mobile) and syncs chats across all of them with end to end encryption. There are different ways to do this. It's just that WhatsApp didn't implement it.