Not the exact term itself, but the significancy of it. The "lying press" is a pejorative used since at least the XIX century [1].
Are we looking for 100% reliability here? Then, yes, we could call the NYT or the WP "fake news". But that is just hyperbole, directed at creating doubt and uncertainty where it does not exist. Once Trump followers had a excuse to label the NYT as "partisan" or "fake", it was easy for Trump to steer the narrative any way he wanted.