I’ve covered many books on game writing here over the years, and I’ve collected and linked a lot of online resources on narrative design and on the history of IF design in particular. I also recently did a post about blogs in this space; and here is one about podcasts.
The Game Design Round Table is a podcast that interviews designers, sometimes including narrative designers. See, for example, this podcast interviewing Emily Grace Buck, who worked at Cognito and Telltale among others, or the results of this search for podcasts involving narrative.
Max and Nick Folkman’s Script Lock podcast is specifically about game writing. I’ve been on it; see also this podcast with Rhianna Pratchett, Jill Murray, and Cara Ellison.
Adventure Games Podcasts covers, well, exactly what you’d expect, including reviews and interviews with designers; their recent episodes include some coverage of NarraScope.
The Short Game covers games that don’t take long to play, but that coverage often touches on story-based games and they have been known to cover IF Comp in past years.
Clash of the Type-Ins is an interactive fiction-specific podcast by Jenni Polodna and Ryan Veeder, in which the participants often play through IF works with their authors, then discuss the work in question. There is a lot of riffing. (I have been on this one also.)
Emily Short's Interactive Storytelling 
Thanks for the recommendations! Script Lock’s a podcast I didn’t realise I’d enjoy as much as I do, and I’m surprised I’d never heard of it before.
Another one to add to the list may be the last few episodes of Designer Notes (as of writing), where Jon Ingold and Meg Jayanth are interviewed on the work they’ve done throughout their career. https://www.idlethumbs.net/designernotes/