I tried doing the chat to cancel. I said multiple times that we wanted to cancel and the person (presumably a person following a script, although they certainly seemed robotic) just kept ignoring that. Eventually I said I'm cancelling, if you charge us, I'll charge it back and took a screenshot of that.
When they charged me, I charged it back. No need for the screenshot, which was mildly disappointing because this was one time where I felt I had proof that I tried to cancel.
We'll never subscribe to The Economist again. If you make it this difficult to leave, better not to start.