Whether the elements in this story could be considered realistic fiction (something that could actually happen) is, I feel, somewhat debatable. There are cases where there has been a sole survivor to a horrific accident. What determines who that survivor is seems to be often little more than luck. Horses can swim for some distance even when carrying a rider and full tack, and it isn't inconceivable that a horse could have made his way to land. As to their relationship on the island, horses are by nature herd animals, and if there are no other horses to be found, a human can be considered a herd-mate, which would explain the bond that they develop. A seasoned jockey knows how to ride a horse to victory in the sense that he or she knows when to use or not use a whip as an aid, when to hold back and when to press, how to achieve the best break out of the starting gate, etc, all purely technical points. The best, most talented rider in the world, however, can't make up for being outclassed by another horse, which could be an explanation for how Alec and The Black won races against riders with substantial experience.
I would not consider The Black Stallion to be realistic or naturalistic fiction. In style and structure, Farley only escapes pure escape fiction by balancing the adventure story with verisimilitude.
To have a young boy be the sole survivor of a sea wreck is a bit much. A swimming horse? To have the boy survive the swim and island stranding is also a stretch. And for a boy to compete in a dangerous horse race and beat a seasoned veteran is not, by definition, realism. Also, the use of superlatives describing the horse gives it mythic, not realistic, qualities.
However, Enotes does suggest two ways in which Farley includes aspects of realism to temper the romance and myth:
1. Style (point of view)
The narrative is structured so that exotic features are balanced by settings and details that are commonplace. The novel features dramatic adventures. Alec experiences a shipwreck, a swim for dear life, an inhospitable island, a series of rides astride an unruly stallion...The stallion enters the novel in the midst of action made more effective by third person description from Alec's point of view.
2. Use of details in description
Farley employs contrast in settings as well, which include exotic and mundane locales. He balances the Black's extraordinary characteristics by portraying him with unremarkable elements of tack. Details related to racing lend verisimilitude, such as Henry's memorabilia of silver cups, newspaper clippings, jockey's clothes and cap. Slower-paced episodes balance dramatic scenes, although Farley never loses sight of elements that generate mystery and excitement.