Why do you find it intensely irritating? Google's a massive company that employees all sorts of different professions and types of people. This puzzle isn't targeting you, seems successful to me.
Well, that's rather my point - the kind of people who would find it irritating are almost certainly not the kind of people they would be targeting with such a puzzle anyway.
Why do I find it irritating? Because it seems both elitist and adolescent, in a child-like "secret society" sort of way.
I would agree, if this was the only method of getting job offers from Google. But since the "traditional" methods via the Careers page, recruiters, etc, are all still perfectly available, this doesn't bother me at all.
That pretty much sums up the people I have met that work in Google engineering. I have only met a few at conferences, but thanks for putting words to the initial feelings I got from them all.