In the interest of being conservative, let us assume this is not an original part of the source of the book.
It is not integral to the story, and does not expound on itself, so it is probably an editorial improvement. The best guess, to my mind, is that this is a suggestion by the 'J' editor of the texts (q.v. http://en.wikipedia.org/wiki/Jahwist).
This editor favors the use of the name Yhwh as a name, preferred over references to God via a title or descriptor, or the two other proper names El and Elohim. He/they/that is the most likely shaping force to give a basis for the meaning of his favorite name, since it makes the other names seem more arbitrary.
People disagree about when the 'J' editing process took place. Estimates range from 950 BC to the 5th century BC. But I think that the latest proposed dates still rule out influence from Parmenides, it seems unlikely any new and foreign idea would have affected scribal decisions that quickly.
It is also dubious how deep the thinking here was meant to be. It may just be reconciling old God names with monotheism. In particular the name of some original "El" god named "Yah", a warrior counterpart of Baal, and who may also be the "Lah" in "Allah" may have gotten reshaped into Yahweh. The epithet "Lord of Hosts" may be a tieback to the old name, so the tradition could have its war-god and eat him too. And it may be emphasized here only as part of the theme of 'Man as Adam as Earth', for God to be what was before Earth, rather than considered in a more deeply philosophical sense.
(Of course modern Christians and Jews, centuries later, do now consider it in that more philosophical sense. 'Ein Sof Aur' and all that. But we have lot of philosophy between then and now.)