Although the film leaves unexplained Riddle's demand that the War Admiral-Seabiscuit match race not use a starting gate, he did have an actual reason: War Admiral loathed starting gates.
The movie never mentions that Seabiscuit and War Admiral were related. Seabiscuit's sire Hard Tack was sired by the great Man o' War as well as War Admiral.
In one of the key moments in the film, a tractor misfires and Red Pollard's horse bolts, breaking his leg. The tractor is a John Deere D or GP. It has a flywheel that has to be turned to start the tractor. The sound it makes attempting to "start up" is that of a car engine turning.