I struggle with agreeing that the podcast is drawing from a cinematic mode; I believe that the podcast is drawing from a much longer tradition of music/sound generally. Especially given that cinema was invented in the 1890s and did not have synchronized sound until 1929, there were was a long history of cinema being visual that still strongly imbues the forms. Sound becomes a tool in the language that is still relatively new.
On the other hand, as you mentioned War of the Worlds and other radio dramas, had a long history of complicating sound and music to create ambience and story. I think it’s more interesting in considering how sound is often not afforded the same academic/creative space as an individual language instead of typically being one that is supplementary or in relation to another established form. I understand the impulse to identify interesting sound techniques as cinematic, but I would push to consider letting sound exists as its own language with its own nuances.