The debate on whether this is a batted or thrown ball is moot. Until it's possessed or becomes dead by rule, it's a batted ball. But this question (TOP vs TOT) award turns on a distinct concept: impetus or force.
What put the ball out of play, the force of the batter or the force of the fielder? If the former, then it's a TOP award; if the latter, then it's a TOT award. The rationale for the differential treatment is that we don't give the offense additional benefit when they themselves cause the ball to leave the field. We do when the defense does it in order to prevent the defense gaining an advantage (such as: extra base hit inside the park, but a fielder kicks the ball out of play to try to get a TOP award that "unscores" runs).
The MLBUM etc. guidance provides philosophy for determining the answer to this question.