Haven't tested to see how they are doing, but that's kinda orthogonal to using tor. Standard cryptography like https uses is meant so any eavesdroppers don't know WHAT you are talking about. But they still know that Alice is talking with Bob. Onion routing, that tor uses, is meant to so eavesdroppers also don't know who is talking to whom. But that's on the eavesdroppers part. If Alice and Bob are talking completely privately, it's completely fine if they are exchanging all the information they want between themselves. The big idea is that attackers don't know what you are doing.

Tor can also hide where Bob's servers are, but not sure if the New York Times would need that bit.

The two things are not directly dependent: for instance, Facebook allows you to connect to your account through Tor. You still have a separate individual authentication (email & password, 2FA) once the connection is established. I believe I have a paying NYT account so I might try if you are interested.

It’s possible that Tor makes it harder to enforce the rule that you can’t read more than X articles per month (which I believe is enforced using cookies and your IP address) but at this early stage, I’m not sure that’s key: people who know how to use Tor generally can easily go around that limitation on https.

If too many people use that loophole to read without a subscription, that means NYTimes would have been instrumental in making Tor mainstream. That would be a major achievement in itself. Enforcing similar consumption limits through Tor would probably be rather experimental, but sounds hardly difficult (especially with the goodwill NYTimes would have most likely gained from Tor developers & supporters).

There you login like normal. Tor can be used to hide from the website owners, and from the network owners between you and the website. If you don't mind that the website knows who you are, you login and identify yourself to them, without letting the network know what you do.

They show the countdown of remaining articles but they have virtually no way of identifying your browser over Tor so all you need is clear cookies and continue to browse anonymously.

The paywall exists on the NYT's onion site as well. But a certain number of articles -- I think 10 -- are free to read each month.