[oligophagy]

i would call them children or pets. the former's apt especially as most cultures conceive of children as somewhat autonomous though still depedent and as not responsible (morally or however) for their behavior.

the distinguishing features seem to be that, though the character is not directly controlled, the player has a monopoly on influences AND the wellbeing or state of the character is of direct concern to the player. hence children. or pets. or whatever.