The classical refer to the fact that th equations of motions of the atoms are integrated according to Newton's 2nd law and that electrons are not accounted for explicitly.
The term "non classical molecular dynamics" is not in use. However, if you would like , you can name the so-called "Ab initio molecular dynamics (AMD)" by "non classical". In AMD , the valence electrons are accounted for explicitly by approximations of Schrödinger equations. Nuclei are still treated "classically " by Newton's 2nd law