One recommendation is to go directly to their website and look at the open roles. Keep in mind that as a very large company, not all roles there have to do with writing/editing. For instance, some roles can be project management, marketing, IT support or development, or even other corporate administrative roles such as in HR or Finance.
Another recommendation would be to look on job boards, such as LinkedIn, and see what types of postings The New York Times or other newspapers have up...this will give you an idea of what types of positions they hire for.
Best of luck with your search!!!