That's the census short definition. To make it workable, obviously you need to be aware of the following understood bits: Known, recognizable origins - usually visible origins. The census definition of Native American actually makes reference to applying only to people maintaining "tribal affiliation or community attachment", and that doesn't stop whites from going "oh, my great-grandmom was rumored to be part Cherokee on account of Black hair and highish cheekbones, so I'm mixed race!", but please be aware that these people are strictly speaking
lying on their census form.
A person in the US of A. This follows, for one thing, from this being the US Census definition. Though you can stretch it to include all countries using similar constructions of race and sharing a similar history, ie much of the Americas - and also to include people elsewhere in the world descended from African-Americans as opposed to direct immigration from Africa, a valid distinction and one drawn by the British Census definitions.
"Black racial groups of Africa" is also highly vague - seems to rule out Berbers as well as immigrated Arabs and Boers and other South Africans, but I don't think they mean to exclude Khoi people. (And what about people who look Khoisanid but speak a Bantu language and would be recognized as "African" - formerly "Native" - in South Africa?) Mostly though, I think they just meant to point out that Papuas, Melanesians, Australian Aboriginals and even the darkest Dravidians are not "Blacks".
This person is in South Africa, a country quite without a history of Blacks being shipped as slaves from another continent, and with its own racial issues (understatement much?) and definitions.
Note that "race" has been pc-renamed "population group". I would assume that your childhood friend's baby is White, but it might also be Other. Before 1994, it would probably have been legally considered Coloured (though maybe not, I'm not really sure), but things have changed in that regard.