OK, I'll try to explain this a little.
First a word about what a capacitor is. It is a electrical component capable of storing an electrical charge. Like a battery, power goes into it at a certain rate, and can be drawn from it at a particular rate. A capacitor's ability to store/give a charge is rated in FARADs. The TR3 capacitor is rated at 0.2microfarads. The capacitor in the video is large (farads, and physically) in comparison, by a factor of at least several thousand.
A Volt-Ohm-Meter is also an electrical device, generally used to measure somewhat passive circuits. The ohm-meter has different scales, but always applies voltage/current into the circuit being measured to determine "passive" resistance. When you use an ohm meter to measure a capacitor, the voltage being applied from the meter causes the capacitor to charge, and appear to change it's resistance. Swapping the leads causes the same thing to happen on the scale, because it first discharges the capacitor, then charges it with the opposite polarity. Different scales of your meter might provide different results. If you have a cheap meter with a "diode" checker that beeps, it employs the highest voltage source, and you can hear the capacitor charge and discharge.
Just because a "new" capicitor acts the same as the old, does not mean anything about either capacitor. Your test equipment is not acting the same way the device is intended to operate -or maybe it is and both capacitors are faulty, but I doubt it. Try another meter and/or another resistance scale.