the parts in the video are Clutch disc and pressure plate, when the disc is worn out the acceleration of the car decrease drastically compared to engine acceleration and causes a little vibration because of the gap being created between the disc, fly wheel and the pressure plate. but when you have a problem in pressure plate sleeves like broken or bend sleeve, it causes the problem mentioned in the video ( vibration when releasing the clutch pedal when moving from stop position. if you experience that problem you should replace your clutch set very soon not to damage the fly wheel mounted to the engine.
I think this may answer my long time query for my car's problem. But just one additional question, why only when the engine gets hot do i encounter vibrations in acceleration from stop.