OK, so it would be ok if an interview someone replied "algorithms are solutions to puzzles" ?

I don't think they are. They are solutions to problems in computer programming. Solving computer programming problems has nothing to do with your aptitude in solving puzzles and brain teasers.

Unfortunately in today's climate it might be realistic to say "algorithms are solutions to interview questions" Although I do believe the more tools you have in your toolbox the better. Knowing algorithms can be incredibly helpful. Same goes for design patterns, language design, etc.

It just seems like a fad to drill people with algorithm questions in interviews even if that skill will never be required for the job. I suppose it reveals to a certain degree whether that person has formal CS training or a personal interest in algorithms.

Algorithms are independent of both puzzles and computer programming. I learned plenty of algorithms in my EE undergrad that were used with a pencil and paper.