The simulation does calculations on the fields only, so it keeps track of the average electron and hole density at each point in space. There is, however, a one-to-one correspondence between the behavior of the fields and the motion of individual particles, which is what makes these animations possible. What I mean by this is the diffusion equation is satisfied by the probability density of a particle undergoing a random walk. So given an electron density that obeys the diffusion-drift equations we can make dots undergo a random walk with drift that turns out to match the given density function (the result is the second set of animations).
The electrons are repelled or attracted by the electric field, which is in turn determined by the average charge density. So two electrons in the animation don't directly repel each other, but the electrons do influence each other through the field.
