ballistic, apparently, refers to the fact that the missile is not fired like a bottle rocket.
The ballistic missiles flight time, arc and trajectory have been calculated, and the missile is aimed for a specific target. The missile may or may not have onboard flight 'correction', or 'tracking', or 'targeting' abilities.
Just the fact it is 'aimed' based on known flight characteristics is enough to warrant the label 'ballistic'.
Since you raise the issue, however, a missile is 'ballistic' if it is subject to no propulsive or direction-changing forces. For example, a golf-ball once it has left the club face or a bullet after it has left the barrel. A rocket is not ballistic before its propellant is exhausted, but then becomes ballistic.