Filing this under a Sanskritic heading is a decision made here rather than a description of Japanese usage, and it is worth stating.
The formula's own term is nembutsu, from a Chinese compound meaning to be mindful of, or to call upon, a buddha. Pure Land teaching does not classify it with the esoteric mantras of Shingon, and Japanese Buddhism has an established vocabulary for that category, which it does not use here. Shinran in particular resisted readings that made the words operate mechanically, and the distinction between reciting for merit and reciting in gratitude is exactly a distinction between the formula as a technique and the formula as an expression.
What makes the comparison defensible is structural: a short fixed formula, repeated, in a devotional register, with an account of what the repetition accomplishes. That is the family resemblance this collection is organised around.
What the comparison risks is importing assumptions. A reader arriving from the Hindu material may expect the sound itself to be efficacious, and Shinran's whole position is that it is not the sound. A reader arriving from Christian devotional repetition may expect an ascetic discipline of counting, and Shin Buddhism explicitly rejects the accumulation of recitations as merit, a rejection aimed at practices within its own tradition that did count.
The atlas's category is a comparative instrument. It has been applied here because the resemblance is real and useful, and the tradition's own name and its own account are given alongside it so that the classification does not silently overwrite them.