There's an easy way to tell.
If the DOJ indicts the NYT, then they believe that the press can be punished for publishing information that they received from a 3rd party.
If the DOJ does nothing or attempts in some manner to indict a leaker to the NYT or attempts to force the NYT to reveal its source(s) so they can be indicted, then the DOJ does not believe that the press can be punished.
We'll see which happens, and from it get some sense of where the correct legal interpretation lies.
If the NY Times knew that the information they received was classified or top secret and that the leaker committed a felony in giving that information to the NY Times, then the NY Times is culpable as an accessory to a felony. If the NY Times knew that the information was classified and they in any way conspired with the leaker to have the information made public through the presses owned by the NY Times, then that makes the NY Times a co-conspirator and a principle and not an accessory.
If the NY Times actually paid for this information and then published it, then it would make the NY Times guilty of espionage
There are a lot of scenarios in which the NY Times itself could be seized and where the editors and the publishers could find themselves behind bars for the rest of their lives.
There is a limit to the freedom of the press. Giving the playbook for the war on terror to the enemy is clearly beyond that limit. The tools we had to detect the positions and the activities of terrorists have been compromised beyond repair. The leaker needs to be publicly executed. The NY Times needs to be seized and the property auctioned off. Finally those responsible for publishing the leak need to be jailed for the rest of their lives.