Here is video of a real gyroball.
As noted by some, gyroballs do not have any unusal movement at all. They have slider-like spin, but the spin axis is directed exactly along the direction of flight instead of being off-center like a quality slider. Because of that, real gyroballs experience zero Magnus force and so they show no lateral movement (i.e., like a spinning bullet). They also do not experience any more downward break than what is caused by gravity (also like a spinning bullet, where the spin axis is pointed in the same direction as the flight direction).
It is certainly not worth the trouble to learn a pitch that is essentially a very hittable hung slider–and that is what a gyroball is. That’s the real reason that nobody uses this pitch–it was sort of a cool physics idea, but it doesn’t do anything that is really useful for a pitcher. (I’m sure hitters would love to see more gyroballs.)
The 2006 Jeff Passan article-link provided earlier in this thread doesn’t do anything at all to explain what a gyroball is. Worse, it quotes Will Carroll’s completely incorrect fantasies about the gyroball. It has been known for some time now that Carroll got the gyroball story completely wrong.