Not sure this makes sense, when you PWM something like an LED, there is no 'leftover DC power'; the energy unused by the LED each cycle is not wasted.

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.

What's the frequency of the 12V AC supply in that video? Is it the same as 110V AC going into the transformer? What is causing the lights to pulse every few seconds?

Yup, same 60hz power mains, it's a simple 10:1 step-down transformer with a resistor and filter cap wall-wart. My camera is recording at 29.97 FPS so you get to watch essentially which sets of diodes on the rectifier are operating on the waveform peak/trough (or would actually see which ones had I had this on an o-scope.) The weird star-trek transporter effect is just the intensity of the lights screwing with the camera + the progressive-scan nature of the camera sensor.

Here's one directly on the mains power. NO CONTROL CIRCUITRY.

https://www.youtube.com/watch?v=AE9QkHmeA-o