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Sounds fairly open theistic to me. On the one hand, I've thought myself that perhaps time is a natural attribute of God; on the other hand, the writer makes many of these statements axiomatically (he states them as though they were axioms) and without any explanation. Ultimately, I am still up in the air. I cannot imagine eternity as 'outside of time' so much as 'age-during' (as the Young's Literal Translation translates "aionion") or ever-lasting--an everlasting succesion of events, if only because it would make heaven a blur. I think I agree with Joshua Harris' dad when he said that "God created time so that everything wouldn't happen at once."

The author also makes the logical leap that for God to foreknow an event before it happened would be for God to cause it, which I would dispute.

And last, he almost sounds like he's denying total depravity in one of those paragraphs ("God did not create sin nor did Adam's fall create sin in every born baby").

Sounds fairly open theistic to me.

I would certainly agree that is one of its effects. Two specifics jumped out at me:

(1) That God knows all which is knowable; and

(2) That God acts (and thinks) "linearly" or sequentially.

Both of these concepts are key insights to the open theism view. The first causes the reader to focus upon the epistemological question of the limits of knowledge. The second takes us away from misleading questions of the 'measurement' of time to the more important sequential/linear question where some facts are dependent of other, earlier facts.

Your phrase ("...an everlasting succesion of events...") catches the concept well. Perhaps that is why the author posits (at least that aspect of) 'time' as a 'natural attribute' of God.

I do not think one can tell from what is said whether the author is an open theist, but he is at least conversant with the issues raised by open theism.