I don't understand your confusion. The only legit way around the pay wall (the pay) is to subscribe to the Times. Since the pay wall more people are subscribing to the online and dead tree versions of the paper. These extra subscribers pay money, which is more revenue for the Times.
Paywall limits access to people who pay (subscribers) => more people pay => Times gets more revenue. What's not to understand?
True, but unless Im mistaken there is an online only subscription, the sole purpose of which is admission past the Paywall. If nothing else, every dime generated from that is related to Times decision to sell an online product.
Additionally, in print media, subscriber revenue surpassing advertiser revenue is huge and not something that would be likely to happen without a successful digital product for a couple reasons.
Beyond that, yes, there's nothing here but correlation. However I think there is enough in the first two paragraphs to make a case.
As a former publishing professional, no - there isn't. If the article were to differentiate between online subscription revenue and print subscription revenue, and were to control for other factors that ALSO drive switch to subscription, then you could make the case that the paywall is "working."
Paywall limits access to people who pay (subscribers) => more people pay => Times gets more revenue. What's not to understand?