That date above is the last day that the New York Times was printed using linotype machines. That word means nothing to many of you. Linotype was a series of inventions in the 19th and 20th century that was used for big newspapers, ones with circulations that could be measured in the millions. Despite the claim, it was not "age old". It had only been in use since 1895. A long time, yes, but not quite a lifetime if you lived to be old.
But times change, and the New York Times with them, and so they switched to computers and a less cumbersome means of laying out a newspaper page and printing it. And nowadays, even people who read the newspaper don't need it printed out.