Yes, there is "leftover DC power" as a diode only allows power in one direction and whatever is left after the LED voltage drop is rectified DC. If I put 12V of LED on a 120V leg, I'll have 108VDC rectified left over after the LEDs take their voltage drop. If no other device uses that power, it just gets dumped out to ground, but it's still unused DC power.

That's not PWM in the video. That's raw mains frequency.