Actually that video gives us no context. When at idle it is not uncommon to see AMD or Intel processors have their speed fluctuate as they lower speed to reduce energy requirements. Even during game play this change can take place as a game puts demand and then reduces demand on the system.
Now under a benchmark or heavy game play this speed tends to stabilize and hold. As for frame drops being created by this during gaming, I am sure there are but the change is so quick that it should not have any real effect on game play. Turning the power savings features off has a couple of effects.
First it increases the power demand of your PC. This is probably not a huge increase in overall cost but it can add up. Most PCs right now at idle can drop below 100 watts of draw, I had a 3820 system overclocked to 4GHz with a HD 7950 and at idle, thanks to power saving features I was drawing around 75 watts. With the power saving features turned off that rose to about 130 watts.
Second it reduces heat, the same system above at idle with power savings was getting down to about 28C, running very cool when it was not needed. By killing the power savings features that idle temp rose to 36C.
The reason people tell you to turn it off when overclocking, specifically the hard core overclocking, is that some of those features are tied top heat, power and TDP of the chip. This means when certain levels are hit the chip reduces speed to bring the parameters back in line. By turning them off you turn off those monitors and get a more stable higher speed even if it is outside those preset perimeters.
Should you turn them off or leave them on? That is a matter of preference. Personally I like my systems cool and quiet, so I leave these features on. Does this mean I might lose a few FPS during game play? Possibly, but to date I have never noticed this lose causing an issue in any game I play.