I take manipulation to mean deliberately mis- or under-informing another to get a result positive for one's self in an interaction between myself and another. Manipulation is a misdirection of another.

I might be able to get more cookies if I don't tell my brother that mother made them today

Telling a story but deliberately leaving out key details so someone will likely think X about us or another instead of Y (i.e., deliberately talking about what the other person did wrong and not mentioning our own actions or talking about our feelings of hurt but not our actions in retaliation so people give us attention where they might not if they had a more complete picture, and knowing that is so).

Running home and telling mother, "Bobby called me a stupidhead!" but not that we first pushed Bobby down and then called him a "crybaby" is trying to manipulate an adult to side with us and get Bobby in trouble with a stronger-than-I-am adult.