Obviously the sort of system pictured is not feasible for the average gardener, however, the use of vertical space is possible if you construct it properly.
The trick would be to construct a series of wooden planters that are offset so that the back edge of each planter gets sun while the sun is at a fairly low angle and then the next planter is constructed partially overhanging the lower one.
The key here would be to support each level well and probably to construct only a limited number of them across the sun's path in kind of a pyramid shape.
The other consideration would be to plant shaded or limited sun crops in the lower bins and full sun crops in the higher bins.
This may be too much of an eyesore for some neighborhoods, but if you live in an area with wide house spacing, or can do it on a rooftop then this seems like a setup that would work well provided it was constructed properly.
This is a crude drawing of what I'm thinking of. What I would do is use concrete in the yellow part in the middle then use cinder blocks or maybe even molded concrete blocks for the front end supports on each layer. This way I would not feel unsafe climbing up to the top of the beds (filled they should be heavy enough not to slide). I am unsure if I would build the top layer in my drawing or not.