NO, it's absolutely not, and it is a reductio ad absurdum argument to claim that it is.
A PRNG (pseudo random number generator) is indeed an algorithm, that with a given seed, will produce a deterministic result. However, the design behind a good PRNG is to ensure that if you don't know the seed, it is very hard (as in, impractical) to determine the upcoming sequence of numbers at any scale.
The Elite Dangerous procedural generator is not like this. While there are almost certainly peturbations put into the system by a PRNG, the overarching procedural system provides results that are at many scales something that is predictable. For instance, the content of a system will be determined in part from its position in the galaxy, this in turn will inform the procedural generator what kind of bodies to generate, and where to generate, which in turn determines what those bodies may be like. See Dr. Ross's video from a couple of years ago about how they run a simulation to create the procedural star systems we see.
While PRNG is undoubtedly used for at least some of the peturbations we might find on a Horizons planet surface, this doesn't mean the whole system is a PRNG. Arguing that because a PRNG is deterministic, and Elite's procedural generation is deterministic, means that they are the same kind of things is a bit like arguing "My dog has four legs, a cat has four legs, therefore my dog is a cat".