Maybe the appropriate term would not be "human", as in an organism that is genetically a member of Homo sapiens, but rather "person", as in an individual capable of human-like thought and entitled to similar rights.
And from a scientific stand point, you're thesis is wrong. "Making something that replicates something else does not in fact make it that thing." It can be important to distinguish between artificial and synthetic intelligence. In scientific nomenclature, artificial would be used to describe something that is created to represent a predefined object or process, while synthetic would actually be that predefined thing, but created through human intervention. Think of the difference between a substance like cubic zirconia and synthetic diamond. Cubic zirconia would be an artificial diamond, in that it closely resembles a diamond but is does not fit the criteria in its chemical structure. Alternatively, synthetic diamonds can be created in labratory settings that are carbon atoms arranged in a crystal structure, and therefore true diamonds.
It is impossible to know at this point whether the constructs present in Bethesda's Fallout are artificial or synthetic intelligence, but we do have several clues. First, the androids are called synths, suggesting the beings are computers designed to operate in a way identically to a human brain, but constructed by humans rather than iological gestation and devolepment. Second, Harkness in FO3 appears to be a synthetic intelligence. Even after a memory wipe, he still demonstrated human-like levels of intelligence: he was still capable of learning, operating and creating memories, suggesting the memory wipe performed on him was similar to the biological condition of amnesia.
It seems likely that these beings do fit a certain philosophical idea of persons, and their origins do not determine whether they deserve rights (much in the same way most would agree that clones, another variety of synthetic human, would deserve rights).
Lastly, I would caution your use of the word "race". It's nondescriptive and has a history of scientifically dishonest misuse. There is no biological definition of race, unless you are using it to mean species, which is a term with its own issues but would better represent the idea you seem to be communicatng.