The MC68008 has an external 8bit data bus. Internal registers are 32bit wide. Typically one means CPUs with 8bit wide registers when one talks about a 8bit CPU, e.g. 6502, 8080 etc.

The Linux kernel requires a MMU for virtual memory support. Here a severly stripped-down version, μClinux, is used which doesn't support virtual memory and (hence) doesn't require a MMU, so any CPU with a 32bit linear address space (implying 32bit wide address registers) could be supported. At the very least a C compiler (supporting GNU extensions) for that CPU is needed.

Said that, there is ELKS (a subset of Linux functionality for 8086) and there is even a (memory-enhanced) C64 running a Linux VM (very, very slowly though).

You could, if you'd emulate a 32b cpu on that 8-bitter.

The real limitation here is memory. Imho it says a lot about modern day software bloat that even an ancient 2.0 series kernel needs ~600KB (ROM/RAM combined). For what, really? That's already a lot of features & almost all hw drivers stripped from it, right? What's that remaining ~600KB code+data doing then?