Yes the New York Times is still relevant, as are many newspapers. After the election, many people realized that television news provides less of the information required to be an informed and involved citizen. Newspapers in general will probably seen an increase in subscriptions. The New York Times has also added to their notoriety for their interview with Trump during a time when he was refusing to hold press conferences.
The New York Times' large spike in readership and subscriptions does indicate that it is still relevant--for now. Newspapers have become increasingly unpopular over the years, but this type of data means that people are still reading. Once all of the election craze dies down, people may become uninterested again. But for now, it seems like people are trying to get data in every way they can.
If Trump didn't think that the New York Times was relevant, he would not be tweeting them after the election. Trump sent them a mean tweet about their reporting after the election. Clearly, even he thinks that they matter. The people still do as well, because so many of them have bought subscriptions.
The only reason that subscriptions have soared at the New York Times is because people want to see what idiotic things the Times will say next. The media has become a joke after this election and the people know that they cannot believe what they read and hear in the media. Newspapers have just become gossip rags and are not taken seriously anymore.