They’re asking that people stay off NYT games and cooking-related pages:
NYT Games and Cooking are BEHIND THE PICKET LINE. Please don’t play or engage with Games or Cooking content while the strike lasts!
News coverage — including election coverage — is NOT behind the picket line. It’s okay to read and share that, though the site and app may very well have problems.
I would assume everything is running via containers which are load balanced and get recreated on crashing. Also I believe Google/Fastly is their CDN (load balancer)