Well I am terribly sorry to give you so much unwanted knowledge.
Saddlebreds grow out of their rack. If it is desired, they are trained to perform the gaits undersaddle. If not, they are not trained to perform them, and they don't do it.
With Saddlebreds it is considerd a Trained Gait. You asked about training non gaited horses to rack. Since most Saddlebreds are trotters(meaning they grow out of thier rack), if they are to rack undersaddle, it must be trained. I'm sorry if I misunderstood. The question seemed pretty clear.
A true rack is a four beat lateral gait performed at speed. Your picture seems like he is, in fact actually racking. He looks quick. The key is speed.
Here is a list and definition of the gaits, from my favorite book:
The walk is a slow, flat footed, four beat gait.
The trot is a two beat gait, in which the diagonal fore and hind legs act together.
The pace . . . Is a rapid, two beat gait in which the lateral fore and hind legs work together.
The amble is a lateral gait usually distinguished from the pace by being slower and morebroken in cadence.
The rack is a fast, flashy, lateral four beat gait. It was once defined by the discarded name "single foot"
The gallop is a fast, three beat gait, in which two diagonal legs are paired, their single beat falling between the successive beats of the other two legs.
The canter is a three beat gait done under restraint. Sequence is the same as the gallop.
The running walk is a slow single-foot or four beat gait, with the break in the impact or rhythm occurring between diagonal fore and hind feet. In the stepping pace, which is also a slow, four beat gait, the break in the impact occurrs between the lateral fore and rear feet.
The foxtrot is a short, broken, nodding, somewhat uncollected trot, a gait sometimes used as a substitute for the running walk.
It is not easy to do, and it is not easy to explain. The best way to know is to actually watch a Saddlebred being gaited. You must affect thier balance. It takes a lot of time, patience, and above all knowledge to be able to teach it.
By the way, those Arab pictures are pretty dang cool!