Their form is based off of the calculations of their own memory, which is demonstrably animate aether, but hey, they're definitely just a rock we drew a smiley face on.
None of the Endless (Endless 10.0, if you will) are merely some 'ideal' brought to life. They are their own memories given new aether to take shape with. Under the in-universe framework of the soul (remember that Codex entry you read?) the soul is separated from its memories in the lifestream, with memories fading into oblivion while the soul is reused. The soul retains no memories, save those of sufficient weight/importance that they are engraved onto it (remember job stones? or Emet's starbursts?). Thus, a soul is not the totality of a given life; rather, it carries on copied fragments of prior lives as it gets tethered to new flesh. (Copied is, admittedly, pure conjecture. Who was the copy? The Exarch crystalized at the top of the tower, or the G'raha we're currently traveling with?) So, it follows that if memory is extracted in whole from the soul, and preserved to be put on new aether, the person is preserved.
You presented the point that the people of Living Memory weren't alive in any sort or manner, and failed to offer any evidence to support it. So, much like an AI, I fear that I must use this data to reject your claims as false, and will not change myself accordingly. Beep-boop.