Maybe caused by several problems:
~~Many kit cars are a mix and match of suspension parts from other cars. A key to good handling is to have the roll centers (front and rear) at similar heights. It's my understanding that many kits Cobras that have live rear axles have the roll centers at very different heights. The front RC being below ground level (on both Fox-based and Mustang II-based cars). And the rear RC being roughly in the center of the differential. This makes them pretty tail-happy (the typically high-powered engines put in these cars can add to this oversteer trait at lower speeds, but it's the mis-matched roll centers that cause the real problems when at higher speeds).
I could not tell if this was a live-axle car (I stopped the vid several times to look at the undercarriage), but if it was, this may have contributed.
~~Also ride height. This car was not real low based on views in the early part of the vid. Increased ride height raises CG, increasing chance of roll over.
~~When the car takes the first part of its CCW spin, the right-side suspension is "loaded" and springs on that side compress. It continues to spin CCW so that the left side of the car is "leading"......just as the right-side springs are releasing their load and "pushing" that side up ("helping" the car to roll). Softer shock valves might aggravate this situation. No way of knowing that from the video, of course.
~~When a car spins like this, a driver is told to "put two feet in". This means to floor the brakes and floor the clutch. The reasoning is that the car will act more predictably, continuing in a more or less straight line. This allows other racers to avoid it. If the brakes are not locked down, the car will lurch and grab as it spins causing and unpredictable path...and sometimes "grabbing" in a fashion that can cause a flip.
Did you see how fast that car was on the straight? To my eye, that amount of speed spoils the fun. This is why I much prefer smaller-engined racers. A friend of mine has offered to let me co-drive a really fast endurance racer this year and I'm really hesitant.......105 mph in my Spridget is fast enough!
And as Steve said, this was a street-car, track day event. That Cobra only had one of those tiny, single-side roll bars popular on street Cobras. At that speed, I'd want a full cage.