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”.
But I’m not an aviator, so what do I know.
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.
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.
Looking at the video, now i'm not sure I haven't been through some dutch rolls also.
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.
Does it actually look different or is it just a different cause for similar movement patterns?
Linked downthread: https://www.youtube.com/watch?v=2tgfkGiHhxs
Especially if close to the ground.
https://www.youtube.com/watch?v=2tgfkGiHhxs
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.