This robot has two hollow interior chambers. When either of these chambers is pressurized it deforms and bends the robot's legs and sides. This bending produces the walking motion. It is similar to how a salamander walks, by balancing itself on a pair of legs diagonal from one another while moving the opposite pair forward.
The basic steps to make one of these quadrupeds are to 3D print all the molds, fill them with silicone, put the resulting parts together to form molds for the waxes, pour the waxes, put the waxes together into the alignment jig, pour one side of the silicone bot, and then pour the other. It might take some trial and error to get a perfect, bubble free robot, but if you've got any mold making or casting experience, chances are you've already got all the expertise you need to make one of these robots in a handful of afternoons spent hacking.