Moiré superlattices can bind several electrons to each potential minimum, forming few-electron "moiré atoms." Using neural quantum states that obey magnetic periodic boundary conditions, include full Landau-level mixing, and treat both spin sectors, we map the ground state of two-electron moiré atoms in a superlattice as a function of moiré depth and magnetic field strength. At strong field each atom is a spin-triplet maximum-density droplet with canonical angular momentum ⟨ L_z⟩=-1 and a persistent circulating current: the rotating counterpart of the "Wigner molecular crystal" recently imaged in moiré superlattices. Deepening the wells drives a singlet-triplet transition to non-rotating spin-singlet atoms whose only current is a weak diamagnetic counter-circulation. The transition moves to deeper wells as the field grows, so depth and field together open a window for the formation of rotors. This is the collective analog of the singlet-triplet transition of two-electron quantum dots. At the transition, the orbital magnetic moments of the atoms reverse sign as their spin polarization switches, a joint signature accessible to magnetometry. If the atoms are instead polarized by other means, such as magnetic proximity coupling, the rotors lock at weak field into a spontaneously ordered crystal of dimers in a pinwheel pattern.