Oh, that thing. Back when I was into legged locomotion, I found out more about that machine than I ever wanted to know. The designer was really into four-bar linkages. The leg mechanism is set up so that one actuator moves the leg in X, one in Y, and one in Z, with a four-bar linkage encoding that into the leg position. This simplifies the control problem, while complicating the mechanics. I suspect they wanted to be…
I don't suppose you have a pointer to an IK paper on the 4-bar linkages do you? Looks like something that might be fun to cons up with servos.