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.
The values in the DOOM table could have been generated by Carmack throwing a dice many times for all we know and just tabulated the results.