The first encounter for much of Europe with African slavery were the millions of Europeans who found themselves sold to the African and Arabic slavers or captured by the Barbary pirates. There were even slaving raids to parts of the European coasts in the early Middle Ages.
Which is not to downplay the effects of the trans Atlantic slave trade, just to put it in context a little.
https://en.m.wikipedia.org/wiki/Barbary_slave_trade https://en.m.wikipedia.org/wiki/Arab_slave_trade
However, as you say, "you are enslaved the moment someone has captured you with the purpose of selling you to another person", which was done in Africa by Africans; many of these people were later (sometimes much later) moved to the coastal areas and sold and transported to Americas, however many were not, and were kept in slavery in Africa.
The original statement focuses solely on the Trans-Atlantic slave trade and implies that the enslavement happened solely for that, which is untrue. Enslaving free people and trading them was a local endeavor done by local rulers and strongmen (the main source of slaves was 'prisoners of war' or robbery raids in local conflicts), though of course them becoming a profitable export commodity significantly increased the amount of "business".
I don't think it's the case that there was nothing racial about the trans-Atlantic slave trade, at least in terms of justifying it to a public who would increasingly be inclined to think that society can tell people not to keep slaves.
Though I would tend to agree that slavery was never only about race, not before the trans-Atlantic trade, and not during.
As far as I'm aware, the majority were sold into slavery in Africa, and then resold elsewhere.
(making the distinction because it's important to why there are still open slave markets in parts of Africa)