2.7 million pixels per second at 35 fps (the cap).
1.4 million pixels per second at 18 fps (~50% of cap).
At the more realistic target of 18 fps, you have 24 clock cycles per pixel. A 486 averaged about 0.8 instructions per clock, so you're looking at 19 instructions per pixel. With a 33 MHz memory bus and the DRAM of the day, you're looking at about 5 clocks for memory latency. That looks like an upper bound of no more than 4 memory operations per pixel.
A convincing 3d renderer averaging 19 instructions and 4 memory operations per pixel. And we're not even counting blit/video delays here. Good lord is that savage optimization work. Carmack is famous for a reason.
P.S. The really scary thought is that Doom would hypothetically run on any 386 machine -- can you imagine painting e.g. 160x120 on a cacheless 20 MHz 386 laptop?