I think you're misunderstanding the theory. You're certainly misapplying it.

Essentially, the archetypal identity theory dealt with repetition of themes and stories across multiple cultures and societies, even ones which had no interaction with each other. For example, the stories of Orpheus from Greek mythology, and Izanagi from Japanese mythology are extremely similar. Both are a story of a man trying to reclaim his wife from the underworld but failing due to his own weakness. However, Japan and Greece had no contact or known shared history. Carl Jung posited that stories such as this were drawn from archetypes that existed in the Collective Unconscious. That both tales were in fact the same story, drawn from the same source, presented through different cultural and personal lenses. Neither Izanagi nor Orpheus would have been a reflection of the other, rather both are expressions of the archetype, which is the original.

The problem is, you can't apply this logic to a single work. Magus and Robo are two different characters in the same universe, the same story, written by the same individuals. Even if they share themes, traits, or even seem to be from a similar archetype (which they're not, the characters have almost nothing in common), their existence in the single continuity pretty clearly illustrates that they are separate entities, especially since the writing itself does nothing to indicate otherwise.

A more accurate archetypal identity statement would be to equate Robo to Vivi. Both are machines constructed for a war against mankind that lose their memory, choose to save the world with a group of heroes, eventually find out about and reject their purpose, and struggle with the concept of their own mortality (Robo through the "the future will be rewritten" scene, and Vivi through his knowledge of the short lifespan of the Black Mages). That is how character archetypes work. Different perspectives and expressions of a single core, which is the archetype.

This doesn't mean that Vivi is Robo or Robo is Vivi. They are both separate, discrete entities, with different personalities, different strengths, and different outcomes. But the theory states that both are drawn from the same archetype. That they have a shared history, shared roots, which are drawn from the Collective Unconscious.

Further, simple equivalence does not equal identity. Just because two characters share traits, themes, or stories does not make them the same character. Repetition of themes and ideals is a common literary tool. It's how plenty of authors set tone and mood for works on the whole. It can also be a result of bad writing and an author not realizing that he's failing to write new characters, and just recycling old ones with new names. That still doesn't make them the same character.