No-one is suggesting that everyone or even the majority of people in North Africa have "black" skin, but I'm awaiting references showing that North Africa was majority white at the time of the Roman empire. The guy in the cartoon has brown skin.
White as in not black. Not as in red-haired blue-eyed WASPs.
Of course it can have "brown skin". Egyptians, Tunisians, and co, including people in Souther Spain, Greece, Italy, Lebanon, the Middle East, and so, had, and still have brown skin, but are not black like e.g. Ethiopians (which ancients also describe), nor are depicted as such.
Well, in Europe (and hopefully modern US) white includes the peoples not considered black (or asian etc).
Arabs for example are still white, Egyptians too, etc. Outside of racist circles were only WASPs or northern europeans were considered white (which was historically the case for most of the 20th century where white was hijacked for "northern European ancestry").
Egyptians for example, are also white. As are Arabs, middle eastern people, etc. But e.g. Ethiopians, or Ghana people are not (the majority of course, not that all citizens are not).
Many of the groups you're mentioning don't even self-identify as white in English-speaking countries. Not really sure what you're trying to get at any more.