Looking at the Doom source, it seems that the actual 3D game view was rendered into a linear buffer, and subsequently blitted onto the mode X surface. Some UI elements went straight to the screen.
(The DOS Doom source was never publicly released, just the Linux port, but there are remnants of some DOS code in the archive. I'm specifically looking at R_DrawSpan in README.asm and V_DrawPatchDirect in v_video.c)
