Should this be "ensure," and not "insure?
I certainly agree with you. That just looks wrong. I would have assumed it was a mistake (even in the New Yorker) if it weren't for this blog post (ca. 2012) that says the New Yorker style guide actually says they use "insure" for both meanings.
See the last paragraph of the answer to the first question on this page:
http://www.writersdigest.com/online-editor/ensure-vs-insure
Why the New Yorker would make such an editorial decision is another question.
British English would still use "ensure". The New Yorker presumably uses the other variety.