I did the Amazon lunch interview back in school. It was every bit as strange as you describe it. It was presented as non-evaluative, but it involved a fair number of behavioral questions and a case study. I'm guessing those questions weren't just my interviewer's way of making small talk.

I had a great time visiting the company, and I ended up with an offer. (Ultimately I decided to go elsewhere, mainly for family reasons that were pressing at the time.) But the lunch interview was completely draining.

By the end of the lunch I'd eaten about two bites of salad. Needless to say, my blood sugar tanked, and it's amazing I made it through the rest of the day. :)