You are right in that に would be more normal. It is an idiosyncratic choice of the author to use で, which means by, with here.
に見えた would just mean the face looked like his own. で見えた gives a nuance that the visual impression given by the face was replaced by his own, i.e., シン was in the state of looking at a mirror when he saw the guy.
The closest (more common) usage of で would be "(の声)で再生される". For example
- For those of my generation, 僕ドラえもん is played with/by/in the voice of Nobuyo Ohyama
(Note: Oyama is the original voice actress of Doraemon, who was replaced quite a while ago. The phrase is characteristic of Doraemon, just like オッスおら悟空 for Goku of Dragonball.).
FYI: A related word (kind of internet slang) is 脳内再生.