It is offer of surrender from AI (btw you can also propose such one). You have to refuse their offer, and propose (force) them to surrender with the list of your terms

The zero war support doesn’t ends war, it allows to force to surrender your opponents, and if would not do it, you will lose stability in your cities, but war still continues.
You can also end war with white peace (you and your opponent refuse demands), or propose your surrender terms before you have lost your support 

Inwoods wrote:

I've never seen this before, so I am a bit puzzled. I just won an early war against green, convincingly. I have a WS of 42, they have zero. I control their only two cities, and they control none of mine. I cannot set the terms of their surrender:

I don't know why this would be.

Is this wrong, as well?

As mentioned by @EsoulBoy (thx), you can refuse and impose your terms, let me add some screenshots to illustrate it.

And also, some context or why is not giving me everything on the first place and just ask for money. Well, imagine you are sending an initial surrender term, you wouldn't offer all your cities at first moment, that is why the initial terms may not be the best ones.

1. Click "Refuse"
2. Click on "Force Surrender"
3. Take everything xD