I'm not going to play semantic games, but, generally, "chattel slavery" involved the purchase of the person themselves as a product - a thing to be owned*. So, the person selling themselves ... questionable; once the 'owner' sells them to someone else, it is definitely "chattel slavery". This is the primary difference between, say, chattel slavery and indentured servitude: an indentured servant is not a thing, but someone who is literally in hock to their 'master'. In indentured servitude, the person is not sold, but the owner of the debt might sell the debt - obligating the servant to change 'masters'. It is also why most places do *not* consider marriage or conscription to be slavery - they don't meet the criteria of treating a person as an object to be owned and the resultant ability to sell them to someone else. Some people might have an attitude that treats non-chattel as if they were, but that doesn't make the institution chattel slavery.
Excepting nukes and slavery. Those two things are clearly delineated as Imperial no-nos in canon. Which is where this discussion started.
*chattel is defined as personal property; tangible, movable property