Mimetic AI imitates a single person, with their particular virtues, idiosyncrasies, and flaws, as opposed to representing a perfected or super-human version of that person.
Example
You can play "against the computer" with the computer trained on all available chess-playing data, and then programmed to make the best possible move in each instance. This is a generic opponent. Or, the computer can be trained narrowly on the data corresponding with an individual player, with all their particularities, all their attitudes, strategies, habits, strengths and weaknesses. So, instead of playing against the computer, you play against Carlsen, Fischer, Karpov...
Here is an academic paper elaborating.