Effectively, everybody in a Civ game is a slave. All of your units do exactly what you tell them to do, all the time. All of your workers in your cities work exactly where you tell them to, and build exactly what you want. It's a Soviet central planner's wet dream.

Colonization also had some mechanics that were sort of a wink-wink, nudge-nudge towards slavery. There was a convict class of settlers, and there were also "converted" natives that you could acquire. If you had missionaries in their settlements, once in a while some religious converts would come over freely. Or you could attack their settlements, which generated lots of "converts"