You’ve probably seen pictures made out of Perler beads, which act as round colored "pixels" that are arranged and melted with an iron. Considering what’s at work here, the process might seem somewhat similar to how a 3D printer arranges melted plastic to build up a structure. It’s so similar, in fact, that hacker knezuld11 converted a delta printer to place beads as images, while a heated bed fuses them together.
It’s quite an ingenious design, as the basic mechanical portion is already available (bead placement and heat), though the details are of course a bit more involved. On top of the printer is an array of 64 bead colors, arranged in bins. These are agitated for feeding down long tubes, and the colors are then selected as needed using a rotary arm stepper arrangement. They're then passed to another placement tube with the help of a “Baby Agitator,” and finally pushed into place.
A Python script matches image pixels to the closest bead color available, then creates a G-code script to place the beads line by line. Two Arduino boards are employed in parallel for processing, and motors are actuated via a RAMBO 1.2 motor controller. Once fused by the heated bed, the new bead-sprite is removed and further melted with heavy objects on top to compress and cement the assembly.
Though the Mario/Yoshi sprite actually printed in the video is excellent, there is an impressive collection of other sprites made with it at 2:18.