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.