At least the linguistic part looks mostly accurate, once you go past the outdated terms. Rather close to what I could find in modern sources, like this one:

A few notes:

It's typically safer, in 2025, to call the group in the Maghreb "Amazigh" than "Berber". The later gets a lot of criticism due to etymology (Latin barbarus "Barbarian").

The page is rather careful to claim that the Amazigh peoples (yup, plural) are there since before the pharaohs; that is likely correct, as their presence in the region likely predates Dynastic Egypt. However you ask "which population arrived in their respective region first?", it's another matter. Odds are that the Egyptians arrived in the Nile before the Amazigh arrived in the Maghreb; simply because odds are that the Proto-Afro-Asiatic original homeland is somewhere between the Levant and the Horn of Africa - it's a huge region but certainly closer to Egypt than to the Maghreb.

"Hamitic" is an outdated term that used to refer to Amazigh, Cushitic, and Egyptian. Nowadays discredited, it doesn't even make sense as a branch, it's from that old arse division of humankind into descendants of the three sons of Noah (Sem/Semites, Ham/"Hamites", Japheth/Europeans). The currently accepted AA branches are Amazigh, Chadic, Cushitic, Egyptian, Omotic, and Semitic.

Linguistically speaking, the Tuareg people are an Amazigh group. It doesn't make sense to list them apart from "Berbers"; it's like listing "Europeans" and "Germans" separately. The Tuareg varieties do belong to a specific Tamazight branch, but it isn't like "the others" are a single unified group.

It's a bit of trivia but people don't often realise that the "Coptic language" in Egypt is a descendant of that "old" Egyptian from Kemet times, that predates the Arabic variety in the region. Nowadays the language is only used liturgically, but it used to be spoken natively up to the 19th century. (Sometimes you see claims that someone was raised speaking Coptic, but it's a lot like raising a kid to speak Latin; the linguistic community was already lost.)

"Bushmen" is another term to be avoided. It's better to call them Khoisan. Calling their languages "click languages" is silly, specially because nearby Bantu languages often also have click consonants.