Let's suppose that the zombie argument smuggles in the assumption that what you're imagining is evidence of reality. Then the argument would look like this:
This still isn't a circular argument. It's just an argument with a false premise, namely premise 2.
More generally, if you think an argument lacks support, that doesn't mean it's circular.
Here's a kind of parody that one might run:
It's the physicalist who's begging the question. The physicalist is saying zombies are impossible. But what's their reason for thinking zombies are impossible? To argue that zombies are impossible, they have to implicitly assume non-physicalism is wrong in order to conclude that it's wrong. Thus, it's circular reasoning.
I reject that either physicalist or non-physicalist is necessarily making a circular argument. They just have different intuitions about whether zombies are possible. You might in fact think that zombies are impossible but then that's the reason to reject the argument, not that it's circular.
It's true that a physicalist would say that zombies are impossible. But that's the point of the argument! It's showing how one of the implications of physicalism is false—zombies are possible.
You might have independent reasons for thinking that zombies are impossible. But the mere fact that the argument is premised on the possibility of zombies doesn't make it circular.
Might be worth addressing Pinker's arguments even if it's unlikely to get him to change his mind. He's an influential guy (Hanania also has a relatively large platform), so it could help to persuade their audience