In 1982 (several years before DOOM), Ken Perlin invented an algorithm meant to produce random numbers that more closely resembled a human's interpretation of "random" numbers (versus those generated by computers). Humans, it seemed, tended to choose a lot of different numbers, whereas random numbers from a CPU actually produced lots of repeating sequences. His work in the field was vital to developing the first 3D shaded graphics in a Hollywood film (Tron), for which he won an Academy Award for Technical Achievement.
Perlin Noise is still used to this day for generating clouds, natural-looking terrains, and other textures that are pleasing to the human brain.
I remember many years ago the iTunes player had to include an option for "humanizing" the randomness of their shuffle play (or whatever they called it).
Turns out that good randomness didn't seem random to people. They might hear three songs in a row from the same album and think "that's not right, it should be random!" Of course, humans often have a different idea of what "random" is.
What I expect from a music player is to play all my songs in random order, such that once a song has been played, it is not picked again until all songs have been played.
There is a difference between randomly picking an element from a list and reordering a list in a random order. This is not a matter of how random really are the random numbers.
One of the classic radio stations in Chicago does this a couple times a year -- they play their entire catalog A-Z. I agree that it does come out pretty nice.
And not just textures or terrain. Apply Perlin noise to a vector field and you create smoothly random motion, which can be used to simulate things like air currents.
To be fair, the key insight to the DOOM prng is that it was used frequently enough for hundreds of mundane events that a player didn't realize (or care) that it wasn't very random at all. There was never a "guess the number" game. A good write-up is here: http://jmtd.net/log/deterministic_doom/
But that does not make the question why the DOOM solution is so much smaller than the perlin noise code more valid. It is simply not the same thing. One is a table of set of generated data, the other a generator of data that can be tabulated.
Perlin Noise is still used to this day for generating clouds, natural-looking terrains, and other textures that are pleasing to the human brain.
Python implementation: https://github.com/caseman/noise/blob/master/perlin.py
Excellent talk by its creator: http://www.noisemachine.com/talk1/