Not really. Doom just requires a 32 bit CPU (maybe someone even kluged it together on a 16 bit platform?) but NetBSD requires a CPU with an MMU.
NetBSD is the slim, small, traditional BSD that has an emphasis on clean code and portability. It's great for small jobs and it'll run on that old SPARC that's collecting dust in the closet. It's simpler than FreeBSD (the industrial strength BSD) and doesn't have the hyper focus on security that OpenBSD does.