James Murphy said his Apex Delivery and Lifting System - or Murphy Mover - is more than just an explanation. It's a nearly energy free way of lifting and moving large objects.There's no getting around the laws of physics. To move a load on a swing, you have to apply force to it. Here's an excellent pendulum simulation you can play around with. Link
It doesn't take much power and doesn't need any major outside energy - just gravity.
This idea might have something going for it: The major problem of the Egyptians should not have been the energy necessary to accelate the blocks, but the friction between the rocks and the ground - they did not use iron tracks and wheels, after all.
Murphy's idea may indeed present a solution to that problem. I guess he proposes to construct a swing on four legs. The front pair of legs allows for some movement with respect to the hind legs. Now, if you set the block into a swinging motion, the center of gravity will alternate between front and hind legs. So, whenever the weight is centered on the front legs, the hind legs come off the ground and can be pushed forward with little effort. When the block rocks back again, the front legs come off the ground and can be pulled forward as well. Thus, the whole contraption "ratchets" forward, possibly even along an incline.
Murphy's contraption will not violate any law of physics. All energy necessary for lifting the block over the height of the incline and to overcome the friction inherent in the mechanism will have to be added by continously pushing the pendulum. (Your confusion might be related to the impression that Murphy claims that this thing would need no energy to lift things, while his claim is simply that you need considerably less energy for moving a suspended object than for sledding it over the ground.)
I can picture that a group of workers is busy with ropes attached to the suspended block, pulling at it in regular invervals to get it into a swinging motion, while another pulls ropes connected to the legs, ratcheting them forward.
That said, I do not think that Murphy's invention has a practical application in contemporary building: A crane is a better solution of overcoming the friction problem - simply by lifting the goods.