As seen in Final Fantasy X, the Yevon Dome was a place with a high density of pyreflies. In places like this, pyreflies will recall moments from the past and project them. The case of Shuyin however, is rather peculiar for not only pyreflies revived his last moments but they started to act on their own.

During the game we are told that we are dealing with a shadow:

Fayth: Shuyin? Just a shadow. It may look like him, but the real Shuyin died long ago. Even after a thousand years, his hate and misery linger on. His feelings grew so strong, they began to act on their own… Eventually, they became a shadow-a shade that wants only to vanish, but cannot.

And after Yu-Ri-Pa’s encounter with Shuyin in the Den of Woe, he is defined as being a dream:

Rikku: Shuyin is no ordinary unsent!
Paine: Seems that way. When he died a thousand years ago, his feelings became intertwined with the pyreflies, creating this…apparition.
Yuna: He’s like a dream…or a nightmare.

We know that he needs to take control over Nooj’s and Baralai’s bodies to reach Vegnagun. Nooj himself says: “He acts through another’s body. Stop the body and you stop him”. It is said that being a shadow Shuyin lacks physical substance and all he can do in his “normal” status is to influence the minds of those around it. In order to interact physically he needs a vessel, more specifically someone that can be easily controlled.

Unfortunately, the game gives little clarification toward this matter. It has been shown in the previous instalment of the game that pyreflies can indeed manifest themselves (by the mean of unsent or fiends), yet it isn’t explained why Shuyin’s pyreflies cannot manifest physically. Moreover, it is not possible to deny that we fight Shuyin himself in the final battle and not merely his bodiless shadow.