A dog is a mammal, but not all mammals are dogs. The paper states "[a] pseudo-random number generator (PRNG) is a deterministic algorithm that produces numbers

A dog is a mammal, but not all mammals are dogs. The paper states "[a] pseudo-random number generator (PRNG) is a deterministic algorithm that produces numbers whose distribution is indistinguishable from uniform." You are asserting the converse, that all deterministic algorithms with uniform distributions are PRNGs.