This Tupolev Tu-154 is demonstrating a gyration known as dutch roll, but a rather more violent example than usual.
The sketchy details of what's going on where are here.
Before I explain why there are several things about this film that make me a bit sceptical about what's happening, I will describe how dutch roll develops.
If an aeroplane gets disturbed in yaw, for example by turbulence acting on the fin or by rudder input, the sideways movement of the tail makes the aircraft pivot around an imaginary vertical axis that passes through the aircraft somewhere near to where the wings meet the fuselage.
Consider a yaw to the right in this Tu-154. "Right yaw" means the tail has swung right, so the nose swings left. The aircraft is effectively beginning to "skid" to the right.
During that right yawing motion the right wing is moving forward relative to the oncoming air slightly faster than the aeroplane's airspeed, and the left wing's airspeed is slightly less than that of the aircraft, which creates a lift differential between the two wings, with greater lift generated by the faster (in this case the right) wing. That lift difference starts the aircraft rolling to the left.
Another factor exacerbating the roll to the left is the fact that, because the wings have a swept-back design, the advancing right wing is presenting a longer profile to the oncoming air than the retarding left wing, generating even more lift differential in the same sense.
(The Tu-154 has another wing design factor known as anhedral - wingtips slightly lower than wing root - which is intended to dampen a tendency to roll with yaw, but not to eliminate it. On the other hand, the fact that the Tu-154's three engines are mounted in the tail means the tail is heavy, so once a swinging motion begins, it takes more time to dampen it).
Back to that first yaw to the right: the swing of the tail to the right stops when the naturally stabilising force of the vertical fin, which tends to keep the aircraft flying straight with no yaw, equals whatever force caused the disturbance in yaw. That is the end of the first yaw/roll cycle.
If, at that point, the pilot applies right rudder, that will add to the fin's force, and the tail will start swinging back to the left, and the yaw/roll effects begin to reverse. If that swing takes the tail through the point of zero yaw, the aircraft is starting another yaw/roll cycle with the forces acting to create right roll instead of the previous left roll. So the aircraft is now dutch-rolling, and under certain circumstances the cycle will keep repeating.
These gyrations also have an effect on pitch, but that is less dramatic.
Now for the sceptic's questions.
The aircraft took off and made a fairly stable climb-out. The dutch-roll didn't start immediately. When the pilots made a final approach, the aircraft had become pretty stable shortly before it landed safely. How was this stability achieved on departure and again on approach when it could not be achieved during other phases of the flight?
If pilots, on a test flight, encounter a major handling problem, they maintain plenty of altitude while they sort it out, and do not attempt an approach until they have tested handling techniques and a configuration which provides the best stability they can achieve. But this aircraft continued dutch rolling until established on short finals.
Maybe gear-down was the stabilising factor? Maybe. The crew left the gear down a long time on departure.
Why was this flight being filmed so assiduously? On the other hand, the film doesn't look like a professionally shot one.
Were they worried about getting this long-parked aircraft airborne again? What gave them cause to worry? Should they have gone ahead if they were worried?
Dutch roll as violent as that shown in the film was not the result of autopilot input or the pilots would (surely?) have tripped the autopilot out. The failure of the yaw damper system would not, alone, cause such dramatic dutch roll.
The investigators will look carefully at pilot input. Whatever force caused the first dutch roll cycle, if pilot input attempting to correct the yaw got out of phase with the swinging motion, the phenomenon known as pilot induced oscillation can set itself up, and this can take the form of dutch roll. It's like a driver attempting to correct a skid, overcorrecting and ending up in a skid the other way.
The best way of overcoming pilot induced oscillation, if there is enough altitude to be safe, is to take hands and feet off the controls and let the aircraft sort itself out.
Now let's see what the investigators say.