Possibly riffing on https://en.wikipedia.org/wiki/Thick_description?
It's almost as though the author thought about and cared about the content and exact words he chose. "Thick or Treat" and "Thickening agents" and "Slim pickings" even immediately evoking imagery of a thin slop gruel in my own head.
By using an unexpected word I think I thought more critically about it, in fact. Had the author used depth I would've immediately had more superficial imagery in my own head.
This doesn't hold for all things - I would, for example, describe a wine as having "depth" but probably not "thickness" because in the case of potables "thickness" also implies a particular sort of textural feel, but I do like the idea of a piece of art as being thick with meaning as opposed to deep. A book which is deep can be reread multiple times, but a book which has thickness just sounds like a book that can live on your bookshelf and be paged through year after year for decades, with not only the content to support it but also the sturdiness to hold up to the use.