I've only read his re-released stories in the "Arrival," compilation, but to me, to describe Chiang as a sci-fi writer is like saying Google is in the computer business.
We inhabit a contemporary world with more technological and social change than the ones which formed the collection of tropes that got authors grouped into sci-fi or cyberpunk in the first place. I don't think devices like time machines and other magic used to create the reflections of characters and situations is sufficient for relegating authors to sci-fi anymore.
Arrival and "Story of your life's" treatment of language and time and experience, and sympathy for the motivations of a super intelligence in "Understand," were succinct descriptions of huge questions. When you compare those to the stupid, 250 page harangues of living national treasures, relegating Chiang to sci-fi puts me into a fit of pique.