This just looks like a way to screen candidates that are competent. Of course they will interview each candidate to assess passion, but they need to make sure they're at least technically competent.

Not really. For instance, I could probably solve the problems, but I don't care enough to try, so I'm obviously not sufficiently passionate about it.

Now if they'd asked me the infinite-grid-of-resistors problem...

Are there competent programmers who could solve puzzles such as these and yet dread going to work every day?

Passion is thinking of better code while you're in the shower, or getting so excited about a new idea that you can't sleep.

Finding a great mind in this way will have a similar outcome to finding a great vocal artist through first round American Idol eliminations.