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.
I recently printed the Fractal Design North Pi case which turned out quite nicely.