The flyback is a transformer device that takes lower voltages and "amplifies" to a high voltage used in the CRT tube to force electrons to the front grid. I don't know what the voltage on the low side is... probably 100 volts or so... and the CRT tube needs like 15000-25000 Volts (no not a typo); to generate the beam that hits the inside phosphor to generate the RGB colors of the monitor.
The flyback is an AC device; but the CRT tube need DC ... so there are diodes and capacitors to convert the AC to DC.
The flyback is unobtanium just like the CRT. If either is damaged; the monitor is landfill.
Caps dry out with Age and Temperature and are usually rated for as low as 5000 hours. The high voltage and high temperature in the monitor chassis leads to pre-mature aging of those caps.
If the Caps short; they can take the flyback with it.
The video you posted looks very much like a fluctuating high voltage rail... which probably means you have bad caps "loading" that rail... which means you're flyback is seriously at risk.
Given you don't know that the monitor and it's high voltage caps have been replaced... you're asking for disappointment when you have to toss that monitor.
One of the first things I did a decade ago when I got my RFM is recap the monitor so "in theory" - mine is good for another 10-15 years. Yours is already past it's shelf date if it hasn't been recapped.