Tatsuya can perhaps be considered a type of Born-Specialized Magician (BS Magician). However, instead of only having one specialized type of magic, he has at least three types of highly-specialized types of magic: Decomposition, Elemental Sight, and Regrowth. The first is considered difficult and high-class while the second and third are unknown to the world at large. Owing to this circumstance, his natural Magic Calculation Area is dominated by these types of magic, particularly Decomposition and Regrowth, rendering him unable to wield other types of Systematic Magic without his artificial MCA.
While Tatsuya's innate abilities are undoubtedly powerful, strictly speaking, at least according to the Yotsuba Family and international standards, they are not "magic", which involves the altering of Eidos instead of simply breaking down and restoring Eidos. His abilities are thus noted by others that know as being more akin to superpowers. This is the main reason why the Yotsuba family treats him as an outcast or a fake Magician and why enemies tend to consider him to be a "monster".