This is a favourite sport of mine to watch--tho' we have little of it in the northeast, unfortunately.
These horses are "thinkers," in that it is the HORSE, not the rider, who has to know which way the cow is going to go. Cutting is a legitimate sport in the USA--mostly from the mid-west to western states, sanctioned by the National Cutting Horse Association. A good cutting horse is worth a tens of thousands of dollars, these days.
Here's a nice introductory video to the sport, from the NCHA:


NotBob
Wow!
That's some show!
You're right, the horse has to know what to do more than the rider by the looks of it.