Think this one through a little more based on what Bob said in post #4.
There are two things we can see without any doubt, and that is that the cue ball follows the object ball at about the same speed and right next to it the whole way, and it follows in the same basic direction.
If the cue ball hit the rail before the object ball, we would know that it was a fuller hit since the cue ball traveled the same basic direction as the object ball. The problem is that if it were a fuller hit it would be absolutely impossible for the cue ball to go anywhere close to the same speed or distance as the object ball did (it probably would have come close to dying at contact in fact) and therefore we can know that the cue ball absolutely could not have hit the rail first even though it happened faster than our eye can see.
But what does explain everything we are seeing is if the cue ball hit the object ball very slightly first and then went into the rail and bounced off in nearly the same direction and speed as the object ball and right behind it.
Just for giggles I also recorded the video and played it frame by frame so I could go as slow as I wanted. One frame shows that the cue ball has not yet hit the rail, nor has the six ball moved yet. The very next frame shows that the cue ball is against the rail, and the six ball is already moving. This is also consistent with the cue ball having hit the object ball first, but we already knew that just by the way the balls reacted.