8-bit is a collective term that refers to an address space that is 8 bits wide.
The first release of Doom, as well as Doom II used 256 color graphics which used an 8-bit palette though there were thousands of shades for color available. Other 8-bit graphics include an 8-bit alpha channel that puts translucency in modern source ports of Doom in whith it makes a total 32-bit graphics mode when combined with 24-bit truecolor space.
The first release of Doom and its derivatives had some 8-bit quality audio modes available for the soundtrack.
8 bits makes up a single byte of data for Doom's software files. A single byte of data also yields 8-bit ASCII characters that represent text strings in DOOM's EXE file data, as well as the ENDOOM lump at the end of the game.
No proper version of Doom used an 8-bit processor as its main chip.