Does this word construction (a meditation on Exodus 3) count as poetry, and if so how would you classify it?
Yes, as concrete poetry, serial poetry, number poetry, and possibly others.
To decide whether a work should or shouldn't be classified as poetry is difficult, bordering on impossible, as there is no standard set of conditions which must be met. It is certainly possible to find definitions of poetry which would include the given construction, e.g. "an art form in which human language is used for its aesthetic qualities in addition to, or instead of, its notional and semantic content." Given the nebulous nature of 'poetry' as a classification, it is typical to err on the side of acceptance.
Similarly, there are many classifications of different types of poetry, more than one of which may apply to a given poem. Additionally, even within a given form, there may be different sets of parameters which could apply (e.g. the well known 5-7-5 format of haiku is not considered as strictly necessary in English).
In this instance, the specialized arrangement of the words adds to the poem (the growing structure, the repetition of "I AM", etc.), which would qualify it as concrete poetry.
Given the number of named poetic forms, it is entirely possible that the given construction would fit into other categories as well.