Earlier quoted context omitted.
Why is this irritating? Google won't hire you iff you solve the puzzle, this is nothing more than a very popular way for institutions to generate free PR.
It is irritating because the "puzzle" involves having a history of searching for stuff that Google Foobar has tagged as relevant. If your Google searches are not linked with your Google account or if you search using different search engines, you're out of the game.
I'm not signed in to Google as a matter of course, and I block their ads, so I provide them very little value. As a result, I won't be able to use "foobar", whatever the hell it is.
Seems fair. Isn't really that irritating, is it? :-)