This collection records the testimony under a heading borrowed from Sanskrit, and the mismatch should be visible rather than smoothed over.
Muslims do not call it a mantra. Islamic vocabulary for such formulas is its own and is precise: shahada for the testimony, dhikr for the recitation of the divine names and short formulas, wird for an assigned sequence, tasbih for the counted glorification. None of these is a translation of the Sanskrit term, and the Sanskrit term carries a metaphysics of sound, of seed syllables and of efficacy that Islamic theology does not share and would in some formulations reject.
What justifies the comparative filing is structural resemblance and nothing more: a short fixed formula, repeated in devotional practice, whose recitation is held to do something. That resemblance is real, it runs across most of the traditions in this collection, and having a single heading for it is what allows the comparison to be made at all.
The risk it carries is specific. A reader who has arrived from the Hindu material may assume that the sound of the Arabic is itself operative in the way a seed syllable is held to be. Islamic theology locates the efficacy in the meaning affirmed and in the intention of the person affirming it, and the formula must be understood by the person saying it for the conversion to be valid. A formula that must be understood is a different kind of object from a formula that need not be.
The classification here is an organisational choice for this collection and should not be read as a claim about Islamic categories.