No in this case the Pico part comes from its use of the Pi Foundation's Pico microcontroller. There are projects[1] that are working on porting PICO-8 to the Picosystem. Unfortunately it will never be fully compatible with the PICO-8 standards as it isn't powerful enough but some games work.
officeplant|2 years ago
[1]https://github.com/yocto-8/yocto-8