This was my early high school days. My friend and I would play Mario 64 DS wirelessly across the hall because we were in different classes but close enough for a WiFi connection. Great times. Also, the Metroid demo included with the console was a fun multiplayer experience.
If you read the article, it is indeed full Linux because the 4004 is running a MIPS emulator that provides the necessary memory management features. Pretty much all of the “run Linux on some old chip incapable of running Linux” projects achieve it via emulating a more featured architecture that Linux supports, not by somehow compiling Linux to natively run on a 4 bit, MMU-less architecture.