I could complain that no journalist seems to have the wherewithal to ask what this means exactly but it isn't really necessary because the inference that one is supposed to draw is plain: "Western-style democracy" in this context becomes a culture-specific product like Coca-Cola or Starbucks that the Americans are crassly exporting, by force if necessary, around the world without regard to differences in culture and tradition.
One wonders what it is about this "style" of democracy that is so objectionable and alien. This business where people get to vote in competitive elections? Or that it allows space for people to protest against the overthrow of a dictatorship that they've never experienced? That in general, despite some obvious failures, governments that have been elected generally have a better human rights record than those that have not been?
Assuming that the aforementioned don't actually object to these features of liberal democracy per se, one can only assume that they mean it isn't appropriate for them; it's really a version of the "Arabs don't do democracy" argument - due to tribal and/or religious traditions or whatever.
My problem with this view is it has been applied in numerous contexts in the past: before Arabs became the focus, the same was said about Asians and Africans; before that, it was used about Catholics; before that, it was said the Germans and the Japanese were unsuited to democratic government; before that, it was said about women; and before that - never forget - it was used about the labouring classes in this country.
That is not to disagree with the idea that the American model isn't necessarily appropriate in all countries at all times but if this is what people mean by "Western-style democracy" they should be less lazy with their terminology and say so. There is no such thing as one "Western" model: some have executive presidencies; some have presidencies and a parliamentary system; some are constitutional monarchies; some are centralized, others federal; some are "consociational" - but what all "Western" systems have in common are competitive elections to representative assemblies, at least some degree of separation of religion from the state and usually some form of entrenched civil rights legislation. If this - rather than the specific American model, with its executive presidency and its legalistic separation of powers - is what critics of democratization think is unsuitable for the Middle East then I think we're entitled to ask why, and ask what other form of democracy they had in mind if they don't like this one?