According to
this table, also from the
New York Times, Nixon garnered 18% of the black vote in 1972. McGovern was considered to be a radical even by many black voters, especially in certain rural areas of the South. Black turnout, moreover, was not that impressive in 1972, and one has to remember that registration rates throughout much of the Deep South were still relatively low, given that less than a decade had passed since the enactment of the Voting Rights Act. I also think there was some residual Republicanism among older black voters, although Nixon obviously did far worse among them than in 1960, when he got 32% of the black vote against Kennedy.
