I found an old PDF file where I sent a friend a copy of the article back when it first came out, but it’s a poor quality scan. Still no luck on finding the original, but haven’t had time to really do an in-depth search for it. However, both in the Equus article and in the link I provided earlier, Dr Bennett explains that Secretariat had a very rare way of galloping. Dogs, cats and most horses etc use a 5 beat gallop (run) called a single-suspension transverse gallop, a rotatory movement. Secretariat and other “exceptional racehorses” had a 6 beat gallop called a “double-suspension gallop which, however, is still transverse rather than rotatory”. Quote from article: “Secretariat ran straight, a fact proven by film study. Straightness during the gallop is an important advantage almost as rare among racehorses as the ability to produce a double-suspension transverse gallop.”
To help give a visual idea of the differences, here’s one of the pages from the Equus article. (apologies in advance for the quality) 
And for visual idea of running straight (again, apologies): 