Multiple two pin multi-color LEDs pattern - how does this work?
I'm afraid we're a smart about this as you are – for all we know (and as you know, from the answer you've linked to), the LED contains some controller itself. It might be controllable by shutting the supply voltage on and off, or by varying the input voltage.

The STC15F204AE is just a run-off-the-mill microcontroller – it was probably chosen for price reasons (it's not an established microcontroller brand, but uses the ancient, yet omnipresent 8051 CPU core architecture.) It executes some software (that we don't know) to send some commands (that we sadly don't know, either) to control the LEDs (which listen to some –unknown– form of commands).