Specifically, he wants me to "explain how this reading differs from the Jewish tradition/exegesis."
Before I begin, I should make two caveats. First of all, I'm not an expert on Ezekiel. In fact, I dare say I've never read a word of it. So this is my thoughts based on my knowledge of Judaism as applied to this interpretation. It does not draw from any source of Rabbinic commentary on Ezekiel to make comparisons, for the simple reason that I've never read any. Second of all, it is important to remember how fractured Jewish theology is in terms of perspective. This trait, already present in the early Rabbinic commentaries (often called the "these and these" principle, referring to God supposedly saying both of the oft conflicting Hillel and Shammai schools ("these and these") are the words of God), became even more prominent in the post-Holocaust era, which led to a significant series of internal critiques and reinterpretations that often differ tremendously with the "normative" tradition. While this makes it difficult to ascribe something as shared amongst Judaism and Christianity ("which Judaism are we talking about?"), it also means that my perspective comes only from a specific branch of Jewish thought, one that I'd say is more accepted than "fringe" but not quite mainstream--a respected minority voice, perhaps? Specifically, I am a adherent to the theology of protest, which holds, among other things, that mankind has an obligation to challenge God over the injustices wrought in His name as opposed to a docile submission to Divine Right. See, e.g., Anson Laytner, Arguing With God: A Jewish Tradition (1998) (Jewish discourse often portrays the relationship between God and man in quasi-legal terms, with mankind pleaing for God to deliver the justice He has promised); David Blumenthal, Facing the Abusing God: A Theology of Protest (1993) (arguing that God's character in the Tanakh (Old Testament) is akin to an abusive father--love and care for His children punctuated by moments of horrific and inexcusable violence); Elie Wiesel, The Trial of God (1995) (describing an imaginary event in which the last survivor of an Anti-Semitic Pogrom places God on trial for violating His covenant); J. Jonathan Schraub, "For the Sins We Have Committed By Theological Rationalizations": Rescuing Job From Normative Religion, 86 SOUNDINGS 431 (2003) (claiming that the book Job is not about Job (eventually) learning to accept God's infinite knowledge and justice as superior to his limited human capacities; but rather about Job's bold protest against Divine Injustice).
Finally, while differences in versions and translation often cause difficulties for interfaith comparisons, as far as I can tell the Jewish translation of the passage in question does not differ materially from the one offered.
With that said, let us proceed.
Some of the post is rather obviously incompatible with Jewish exegesis. The Christian foregrounding prior to the interpretation, for one. This passage, too, would seem a little out of place in a typical Jewish tract:
Israel was severely disciplined not in spite of the fact that they were the chosen people of God, but because they were the chosen people of God. At the present time that responsibility has been transferred to the Church: we are now the elect of God and we are charged with reflecting His glory and proclaiming His salvation. The privilege, the responsibility, the consequences are all enormous.
However, even beyond that I think there are significant differences in the Jewish response to the passage.
I think that the backgrounding of events we'd agree on. God was upset with Jews forsaking Him and His Torah, and so he was gearing for some smotin'. However, the conclusions I think we come to almost exact opposite. The author of this commentary believes that the Jews were lulled by the temporal aspects of their faith (IE, the Temple), and that was why the message was sent. This is in keeping with the generic Christian view of spiritual over temporal. Indeed, that is the theme of his entire post--he concludes by saying:
The day for the church will one day come when the bodies of Christians will be scattered before the idols of their hearts - banks, governments, stadiums, schools - in a demonstration of the utter inability of any of these things to save. Perhaps not literally slaughtered, but certainly just as effectively crushed. Eternally secure; temporally undone and destroyed.
The point then would be that true faith needs nothing material on this earth, it is solely a facet of an individuals relationship with God.
Jewish exegesis would take the opposite view. Specifically, they'd focus on how the Jews were in violation of God's laws on earth. Following or not following the law is a material act--the Jewish conception of doing Mitzvot is not just because God said so and we should honor God, but rather to create a more just world (Tikkun Olam, repairing the world). The Jewish conclusion would be a redoubling of effort toward the material aspects of life that make it tolerable or intolerable--MORE justice, MORE tzedakkah, MORE love for ones neighbor. It is an explicitly temporal philosophy that stands in stark contrast to the harsh This Life/After Life split found in the Christian commentary.
That's the "stock" difference (although I use the term cautiously). My branch of Jewish thought would agree, but add another split. Both the "stock" Jewish story and the Christian counterstory assume that God is perfectly within His rights to undertake this action. This is either because He's God, and can do whatever he wants or, if pressed for a reason, that a) the people deserved it because they abdicated the law (Jewish version) or b) that God wasn't taking anything of value anyway, because it was all temporal and ultimately irrelevant (Christian version).
Protestors would question whether or not God was right at all to do this. As the Christian commentator puts it:
God is very serious about two things: sin and His holiness. He is not going to tolerate the sins of His people indefinitely and He is not going to compromise His holiness. God is serious about sin because He is serious about His holiness: He will purge the evil in His people no matter what it takes or what it costs them in temporal terms. By His terrible acts of judgment upon His people, God will (1) remind His people that He - and He alone - is God and that He will not share His glory with another, and (2) demonstrate to the unbelievers nearby that He is deathly serious about these things even if His people are not. If they will not reflect His holiness, then He will make them an object lesson by which others may learn to fear Him.
One might note that this seems rather egomaniacal by God. He cares about Himself and "His Holiness," and He cares about sin because it compromises His holiness. Essentially, He finds it rather like mocking Him. But the punishment seems vastly disproportionate to the crime. Like the abusive father upset that his kids aren't showing him proper respect, He flies off the handle and vows to exact vengeance, in this case, specifically vengeance in the form of mass murder. And it follows a pattern of behavior by God in the Bible--professed love for his children (kind Father) when they are good, but terrifying rage when they disappoint Him (abusive Father). Although we might say generically that parents have the right to expect obedience and respect from their children, we don't carry this to the conclusion that they can abuse their children for disobeying.
While the Christian subtext to Ezekiel is that God isn't taking anything that matters (it's only temporal, and even lives are just returned to Him), Judaism doesn't have that out. The temporal world and (especially) human life DOES matter, and cannot be dealt with so casually. Indeed, the Jewish doctrine of Pikuach Ha'Nefesh, to save a life, explicitly exempts one from any Biblical law in order to save a life. This principle has been cross-applied to God Himself--recall how Abraham argued with God to spare the lives of innocents in Sodom and Gommorah.
While this latter interpretation is more radical, both the standard and protest Jewish interpretations seem to be materially different from the Christian one.
Hope that helps!