Striking is not damaging the workplace in any way other than removing employees. Actively misconfiguring equipment is a dismissable offense in pretty much every situation I've ever seen. It can also be considered criminal.
I see your point, but I don't see how that might be damaging. Deleting data would be damaging. Putting a flamboyant rant instead of the home page would be damaging. But this, to my mind, amounts closing the factory gates and writing "Strike" on them with a piece of chalk. Rolling it back would amount to commenting out a line or two in a config file, maybe even.carefully commented for that purpose.
Absent human meddling, computers tend to just chug along doing their work once set up. In fact, I would be surprised if NYT weren't under a code freeze for the event regardless of the strike. So this would be more like shutting down the automated assembly lines on the way out (knowing that they're designed to run with no human operator and are never supposed to be shut down) rather than just leaving.
Deliberately making your employer's services unavailable for anything other than authorized reasons is quite simply sabotage, mischievousness, or any other thing (IANAL) that could be used to describe the act. It's not like someone make a bad configuration file that went unnoticed and pushed to the core routers to bring down the network as a mistake. This was a consciously made act to disrupt the company's services out of spite because employee didn't get something they wanted.
