Dulloldfart
Squirrel Extraordinaire
After the rockets engines turn off, it follows a parabolic or elliptical (not hyperbolic) path, and that is ballistic, I think. If fluffy was flying in the atmosphere with wings, straight and level, that would not be ballistic.
Ignoring the fluffy aspects of it, the general usage matches more the explosive powered part of the flight than the free-fall remainder.
Paul