I think "detective" is a theme and Information Games are a format / design principle. They seem to fit great together, but I've never tried making one so who knows.

The character limit was too low for a thank you. Thank you for the great answer :)

I also thought about info games as "real" detective games as they truly incorporate the investigation theme into the design. Then I was confused about whether info games were only a subgenre, but with your approach of differentiating between "design genre" and "theme genre" it makes much more sense!