So, lemme get this right. You click "Shutdown", your PC shuts down Windows and turns off the PC, which also shuts off your peripherals, which seem to be electrically powered, not PC powered. I've never seen a power strip that does that. The only way to turn off all my peripherals at once is to press the master switch on my power center, except for my desktop speakers, which are fully PC powered.

You are correct, this one came from Staples, but I understand there are others out these. It's a wonderful convenience.
I also bought a bunch of 8" long extension cords so all those funny shaped voltage converters and shit could plug into one strip.

Just saw one in Walmart on clearance sale for $34.

I had one, but it didn't really work. I wonder if my PC was so much of a power leech that the strip didn't reliably recognize it as "off".

Or maybe it was just defective.

A power controller in a PC is always on. If that power strip detects as little as 5 milliamps, then it would not power off other receptacles.

Replace a computer connection with a 7 watt and later with a 100 watt incandescent bulb (not LED or CFL). To discover what that power strip sees as power on and power off.