I am going to do something apparently silly, and answer my own question.
That's because the question is not originally mine, but by a user named Maria BI. She asked this in Skeptics stackexchange, and people there voted to migrate it here (which seems reasonable; it is a question about History, after all).
But then the question was closed here (and so much closed that I couldn't even comment or find the discussion about its closure). My impression is that this was a knee-jerk reaction, and that a huge part of such reaction is due to Maria BI being a newbie. Such impression is reinforced by the fact that I essentially reasked the question, and it seems to be well accepted now.
I was hoping that I would not have to answer it, as other people would give adequate answers. But I am not satisfied by the answers so far, which generally suffer from two problems: 1. the identification of any kind of forced labour with slavery - which may be morally satisfactory, but is historically wrong - and 2. the consequent idea that "slavery was the rule after the invention of agriculture and before the industrial revolution".
Those ideas are false. In part, they stem from the fact that most ancient historiography we have access to is either Greek or Roman; Rome and Greece were societies based on slavery, and their writers tended to see "slavery" in other social formations. This is not unusual - Portuguese chroniclers wrote about Tupi-Guarani "kings", even though the latter never had anything similar to a monarchy; and modern writers often talk of "capital" in obviously pre-capitalist societies.
In fact, slavery was rather the exception than the rule in human history (which is not to say that forced labour was rare). For instance, Perry Anderson writes (in Passages from Antiquity to Feudalism, and citing Finley, Between Slavery and Freedom):
The originality of this mode of production must be underlined. Slavery
itself had existed in various forms throughout Near Eastern Antiquity
(as it was later to do elsewhere in Asia): but it had always been one
juridically impure condition - frequently taking the form of debt
bondage or penal labour - among other mixed types of servitude,
forming merely a very low category in an amorphous continuum of
dependence and unfreedom that stretched well up the social scale
Most agricultural, pre-industrial societies relied in the exploitation of peasants through rent, ie, the concession of land against the payment of dues either in labour, or as a part of agricultural production, or in money. We have discussed it here.
As far as I am informed, actually only the Greek and Roman civilisations were extensively based on slavery (the kingdom of Palmira was the most probable exception). Slavery did exist in other civilisations, but was for the most part exceptional, and usually restricted to personal services, not being the main form of labour in agriculture. Again, I refer to Anderson:
it was a residual phenomenon that
existed on the edges of the main rural work force. The Sumerian,
Babylonian, Assyrian and Egyptian Empires - riverine states built on
intensive, irrigated agriculture that contrasted with the light, dry-soil
farming of the later Mediterranean world - were not slave economies,
and their legal systems lacked any sharply separate conception of
chattel property. It was the Greek city-states that first rendered slavery
absolute in form and dominant in extent, thereby transforming it from
an ancillary facility into a systematic mode of production.
Even in Greece and Rome, the full development of slavery was only possible due to the reforms that abolished debt-slavery. As Anderson says,
it was not fortuitous that the salvation of the independent
peasantry and the cancellation of debt bondage were promptly followed
by a novel and steep increase in the use of slave-labour, both in the
towns and countryside of classical Greece. For once the extremes of
social polarization were blocked within the Hellenic communities,
recourse to slave imports was logical to solve labour shortages for the
Now to the substance:
There was some kind of "slavery" in Subsaharian Africa before European colonialism set foot there. It completely differed in kind, substance, and scope, from slavery as we know it in the "new world" - United States, Cuba, Brazil. For instance, the Portcities website for "Bristol and Transatlantic Slavery" explains this as
Slavery existed in Africa, but it was not the same type of slavery that the Europeans introduced. The European form was called chattel slavery. A chattel slave is a piece of property, with no rights. Slavery within Africa was different. A slave might be enslaved in order to pay off a debt or pay for a crime. Slaves in Africa lost the protection of their family and their place in society through enslavement. But eventually they or their children might become part of their master’s family and become free. This was unlike chattel slavery, in which enslaved Africans were slaves for life, as were their children and grandchildren.
It was - of course - not linked with racialism, it was usually restricted to personal services, particularly to the local nobilities, and was subjected to little trade, if at all. Slaves were essentially war booty. Noblemen probably make them gifts for friends or foes, but the practice of making slaves for the express purpose of selling them only took off once European colonialism entered the equation. There was little slave labour in agriculture or husbandry; the women would serve in the harems of conquering lords, both men and women would be domestic servants in the great houses.
So yes, European slavetraders certainly belaboured upon an existing tradition of enslaving conquered people; but to them "slavery" meant something completely different than to African local warlords - quite probably, something completely unimaginable from the perspective of that people.
Islam certainly does not forbid slavery; it merely restricts it to non-believers. What Islam does forbid is racial discrimination, so slavery in the Muslism world had little to do with race. Muslism warriors and merchants would enslave "Blacks", as in subsaharian Africans; but they would also enslave "whites" like Serbians or Bulgarians. They did establish routes for slave trade, but those usually had to do with the East, via Indian Ocean, not with Europe or, much less, the new world (so, the Europeans did not inherit such routes, but created new ones). Slavery in Muslism domains also remained basically an issue of services, not of agriculture, and the status of slaves in such places was very different from their status in the West (to the point that the ruling layer of Egypt, at some point, was actually composed of people who were technically slaves; see, for instance, The Mamluks in Egyptian Politics and Society, edited by Thomas Philipp and Ulrich Haarman).
For the sheer scale of trans-Atlantic slave trade vis-a-vis the Middle Eastern (trans-Saharian, Red Sea, trans-Indic), Nathan Nunn (scholar.harvard.edu/nunn/files/hup_africa_slave_trade10.pdf) puts figures at 12 million traficked Africans in the trans-Atlantic, within a total of 18 million in all routes from the 15th to the 19th century; so the average annual impact of the Atlantic trade would twice as important as that of all Arab-dominated routes; but notice that figures for the trans-Atlantic trade sharply increased in time, so the brunt of the manhunt was in the century between 1750 and 1850, when more than 7,500,000 slaves were trafficked, and it became so significative and devastating that even the sex ratio in West Africa was disrupted (see the Transatlantic Slave Trade Database.)
Now a bit of ad hominem: Stefan Molyneaux, is spite of having formal academic training as a historian, is what would be best called a "crank": someone who spouses "non-mainstream" (to say the least) views on history, for the end of both political propaganda and personal self-promotion. So whatever he writes or youtubes should be taken with a huge amount of salt - probably enough to boost Utah's economy. Regarding his political stances, they seem to be served by a kind of revisionism that denies the excepcionality of European colonialism, and tries to "blame" slavery on Muslims - if not on Blacks themselves.