It still isn't magic by technicality.
Healing magic in this world works by replenishing the body with new "life force", which is this world equivalent of Ki, to make up for what has been lost. What he did was simply applying that logic to his own breathing technique to temporarily fill his body with clean "Ki" which yields the same effect as low-tier holy magic. I said low-tier because it only allowed him to touch the intangible spirit, everything else was still done with his fists.
Even irl breathing is a core part of meditation and many medical/scientific papers have already proven the existence of "life force" after studying Indian gurus. So no, it's not magic.