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).