On that page I see this:

> To change or cancel your subscription, please contact Customer Care.

This is only for deleting your entire account. It says right there at the top of the form

"To change or cancel your subscription, please contact Customer Care."

As a free user, you still need an account to read certain free articles. So it's not really the same as canceling your subscription.

I also wouldn't be surprised if they deleted your account but kept billing you.

I've tried using this form several times. They send me an email afterward telling me they won't delete my account. (This is despite me living in a jurisdiction where deleting my account is legally non-optional.)

NY Times needs to get their shit together.