I feel like “roll” is a bad word for what’s happening here. In my brain, when I hear “roll”, I’m thinking a 360 degree rotation in either the vertical or horizontal axis (or both).
This is far from that (even in the real life footage linked in the sibling comments). This is more like a “Dutch wobble” or “tilt”.
What you describe might be called a loop. In aviation, “roll” describes any rotation (not necessarily full 360) around the longitudinal axis, as “yaw” around the vertical and “pitch” around the lateral axis.
ETA: 360 degrees pitch is a looping, 360 degrees roll is a aileron roll or slow roll, a 360 degrees roll and pitch is a barrel roll, and 360 degrees yaw is “a 360”, ie a full circle turn.
"Roll" is the name for one of the three axes in aviation. "Vertical" and "horizontal" aren't very descriptive in three dimensions.
You could reasonably call yaw the "horizontal axis", but then assigning "vertical" to either of roll or pitch – and what do you call the other one then? They're arguably both vertical, depending on which side you look at the plane from! Additionally, at least "horizontal" implies an Earth-centered focus, which doesn't help while in, say, a barrel roll :)
Best to avoid the ambiguity entirely and use specific terms, just like how port and starboard avoid the "my left/right or yours" ambiguity nicely by always referring to the ship's frame of reference.
Dutch roll was particularly pernicious with trijets. It has to do with thrust vs lift vectors having different offsets (origins) relative to the cg. Sometimes they would add stabilizers to the tail to correct for this, but eventually manufacturers gave up on the design.
Imagine you are in the cockpit at the top of the plane and your view/perspective - for a layman like me this would seem and feel like the flight is completely out of control. Even the passengers are bound to experience dramatic movements similar to severe turbulence I guess.
Dutch Roll is a coupling of yawing and rolling dynamic modes, and is a product of the aircraft's aerodynamics. If the aircraft is disturbed off a steady-state path either by control input, changing winds, or turbulence, then it should return back to it's steady-state path with oscillations that quickly dampen. Dutch Roll is a phenomenon where these oscillations grow rather than dampen as a result of out-of-phase yaw and roll modes.
So Dutch Roll can be triggered by turbulence/wind, but the Dutch Roll itself is the result of something going wrong in reaction to that stimulus. This is different than the aircraft just being batted around by turbulence.
Just being batted around by turbulence looks different if you know what you're looking for (although what to look for might be only obvious when looking at accelerometer data). Again, Dutch Roll is a very specific phenomenon as a result of coupling between the roll and yaw dynamic modes. The risk of Dutch Roll is that these oscillations can grow even without further stimulus rather than just dampen out.
The FAA reported: "AIRCRAFT EXPERIENCED A DUTCH ROLL, REGAINED CONTROL AND POST FLIGHT INSPECTION REVEALED DAMAGE TO THE STANDBY PCU, OAKLAND, CA." and stated the aircraft sustained substantial damage, the occurrence was rated an accident.
The PCU in this context is the part that moves the rudder. PCU issues were common on the 737 in the 90s[0] although that's... probably?... not relevant here.
For what its worth, that's very unlikely in the last decade or so. More likely to be moderate turbulence, which would be nearly indistinguishable in a non-severe event.
https://youtu.be/Zmjam1evDD4