"there was no history in Africa and N and S America"
By most definitions of history that is a true statement.
Wonderful and rich civilizations may have filled those blanks areas, but if there were no written accounts that survive to the modern day (or at the very least oral traditions that were eventually written down), they are by definition "pre-historic". The study of those peoples is left to the realm of archaeology and anthropology, not history. We know even less about those pre-historic civilizations that built using materials that do not stand the test of time (wood, thatch, mud, etc).
But we do know, it's just not shown on this page! E.g. the Mayan and Aztec civilisations. There is a massive amount of history than can be traced to the physical structures they built.
One cannot seriously claim that there was no History in Britain until the Romans arrived (or that nothing was / is known about it), which is what this map suggests. The ancient Greek Pytheas [0] visited Britain in approx 330 BC.
The map clearly shows Mayan and Teotihuacanan civilizations in pre-colonial eras. Is the map perfect? Of course not, but I'm confused by your insistence that it's ignoring Mayan and Aztec civilizations when it plainly shows them and their predecessors.
By most definitions of history that is a true statement.
Wonderful and rich civilizations may have filled those blanks areas, but if there were no written accounts that survive to the modern day (or at the very least oral traditions that were eventually written down), they are by definition "pre-historic". The study of those peoples is left to the realm of archaeology and anthropology, not history. We know even less about those pre-historic civilizations that built using materials that do not stand the test of time (wood, thatch, mud, etc).