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The entire worker benefit of the union is collective bargaining and NYT has rejected working with the unions.
What actually happens is prevailing trends basically continue. Management can still hire people, etc. but must continue more or less as before unless they are willing to negotiate those specific changes.
A union that's recognized but doesn't have a contract may as well not be a union at all. Basically the only power they can exercise is to strike.
In this case "secure a contract" means terms that are somehow perceived as more favorable than employment-at-will.