The NYT is called liberal, but more correctly it's pro-establishment/pro-government left-of-American-center.
They are personified by the Clinton family, yet are more pro-Bush than say pro-BernieSanders or pro-GaryJohnson.
With Trump's alternate-establishment weirdness and the extent polarization of modern US politics, the right wing is rejecting the NYT and thus pushing them farther left to maintain readership by catering to replacement readers.