You're exactly right and I'll go a bit further. As someone who's had a good bit of time on track in all sorts of cars, there are a few specific things that are easy to pick out:
1) Driver did not follow CPR. CPR = Correct-Pause-Recover. This is a basic technique that should be taught to all drivers, but is currently only taught in some driving schools. Basically the person in the video correct, then over-corrected in the opposite direction.
2) Driver lifted throttle, initiating a spin. In FWD cars it's very important to keep on the throttle. This keeps the front tires rolling in the correct direction and keeps the weight transferred to the rear tires. Lifting (as shown in the video) causes the front tires to "brake" and makes the rear end light. That combined with over-correction = spin.
3) Did not follow the "In a spin, two feet in" rule. If the driver would have gone "both feet in" (brake and clutch) then the car would have just slid down-track a ways and not have darted off track.
4) WIthout a better video angle, it's hard to tell, but novice drivers frequently have issues with looking in the wrong place. I can almost guarantee you that once the car started to spin, the driver was looking at the wall. You're going to drive where you look.
I feel bad for the guy, I really do. A little bit more/better driving training would have avoided this.
To anyone who's interested in knowing what should have been done:
1) Stay on throttle and correct the initial spin
2) Stay 2-wheels off track until the car has settled, then ease it back on track.
3) If all that doesn't work, brake and clutch 100% and look straight down the road (even if that means looking far to the right/left)
I had the benefit of learning all of this on tracks with very little to hit, in a car that was very very cheap with awesome instructors.