Mike, the circuit seems to follow the datasheet's recommendation, third page.
https://frack.nl/w/images/3/33/LPD8806_datasheet.pdfOnly the LED rail is connected to 12volts. (3x 3.3volt LED in series?)
And every single chip is supplied from a resistor and 5v1 zener to ground.
The IC's supply pin is roughly in the middle, left hand side.
You can just see the connection to the resistor and melf (zener?) diode.
I think this strip uses
six 5050 LEDs per IC. Each package containing three LED chips
of the same colour.
And the Adafruit strip uses
two RGB 5050 LEDs per IC.
Single LED explains the 5volt LED rail.
Adafruit's strip can mix colours (RGB LEDs). This strip can't.
But I could be wrong...
Maybe the owner can confirm this.
Leo..