Some versions of Doom ran on 16-bit high color graphics modes of some computer systems.
Some versions of Doom use 16-bit quality audio for its sound.
32-bit hardware extensions from and with 16-bit hardware and software
The earliest version of Doom and Doom II which was for DOS, which itself is a 16-bit operating system, used an internal utility called DOS/4GW which allowed entertainment software with 32-bit quality gameplay to run on a 16-bit operating system. This was all thanks to the minimum requirement for an Intel 386 processor which was the first 32-bit x86 processor. When Doom, Doom II and Final Doom were released onto Windows 95, Windows 95 itself was a hybrid 32-bit/16-bit operating system, though Doom95 itself was a Win32 application, and Windows 95 required a 32-bit x86 processor.
After the release of Doom II on the PC, the original three episodes were released to some 16-bit consoles that used special 32-bit enhancement hardware. For the Sega Genesis, the 32X allowed for additional address space to enable Doom to run its demanding resources of the time which a 16-bit system wouldn't have handled. Whereas with the SNES, the Super FX 2 chip inside the DOOM cartridge allowed for an internal co-processor of the game cartridge to eliminate the need for bulky addons for the aging SNES.
Later on, the practice of attaching 32-bit technology to 16-bit hardware and software computer archetecture became obsolete when later releases of classic Doom were ported to pure 32-bit platforms. Classic Doom's sequel Doom 3, as well as other id products like Quake were largely ported to 32-bit platforms, though Quake's initial DOS release itself was simply another example of a 32-bit DOS/4GW application using DOS as an underlying 16-bit operating system as a bootloader.
Later on when source ports were being released for Doom, a source port for the Atari ST was released, and yet the Atari ST itself was a hybrid 16-bit/32-bit home computer where the ST stood for "S"ixteen/"T"hirty-two.