I'd say there's a problem with the CVT, maybe with the clutch.
At idle or when the motor is off, the belt should run at the edge of the rear pulley and at a really small radius around the front pulley, as seen in this picture:
When speeding up, the belt should should rise in the front pulley and sink into the rear pulley, which causes the change in transmission ratio.
Let's see how it works: The front pulley consists of a simple outer sheave, while the inner on consists of two plates with typically six cylindrical weights (green) between them:
The centrifugal force of the running motor pushes the weights outwards and so the plates (of the inner sheave!) apart, making the pulley narrow and the belt rising.
As counter-force, the rear pulley contains a big spring which pushes its sheaves together.
Your belt runs at about the same, constant radius around both pulleys, which is strange. I'd say either something is wrong with the weights, seizing the front pulley at a fixed position, or the spring is broken, so there's not enough counter-force.
The front pulley can easily be taken apart (you already did it to change the belt, right?). Inspect the inner sheave, if it can move, and if the weights are still cylindrical. (They wear out over time, but can be damaged by an event like a snapping belt. If you need to replace them: They have a specific weight, determining the motor RPM. You need to know that weight, too)
Inspection of the rear pulley is a little more difficult. As a first test on a 50cm³ scooter, one would try to pull the sheaves apart by hand, which should be hard, but possible. I guess it's impossible for a 250cm³ scooter, and you have to disassemble the pulley to check it. Therefore, you first have to disassemble...
A scooter clutch is similar to a drum brake, except that the inner part with the pads is connected to the pulley and so rotating. The pads are kept back by small springs, but with increasing RPM, the pads move outwards, and start slipping at the drum. With even more RPM, they don't slip any more, and the clutch is fully engaged.
The drum is the outer part beneath rear pulley. It is connected to the wheel by a transmission, and when the wheel can spin freely, you should be able to turn the drum without any force.
The drum is shattering in your video, because it is right at the point between slipping and idle. This is strange, because even when your motor is at idle, the RPM of the rear pulley should be high enough for a completely engaged clutch due to your odd CVT ratio.
Since you have to disassemble the clutch anyway, check it for obvious damages.
I'm wondering: A 250cm³ motor should be strong enough to accelerate a free spinning wheel even when the CVT is seized in a "high gear".
I can imagine that the clutch tries to engange at too low motor RPM, when the motor doesn't have any power. This could cause the motor to bog, but to stop?
May be, there's even more damage, and your motor doesn't have any power?
And one evil question: You checked the size of the belt four times. Size means length and width, and you checked both, right?