I suspect that Adam and John don't need the money they make from the podcast to pay their bills, so I'm not really sure what "it's working" means to them. The article you linked to doesn't mention any specifics.
I like the show, the model seems to work although the newsletter is constantly pushing people for more donations. Their wording makes it seem like they are on the edge of being sustainable all the time. This could be true of course.
If you take the time to listen to them longer , > 10 podcasts or so your start to pick up on the type of thinking they have, it really can be refreshing and No Agenda should certainly be part of a healthy news diet, as they call it.
By the way, strange to see nobody mention TWIT, I enjoy it every week, they seem to do very well. Also, the Jupiter Broadcasting network (Linux Action Show, Linux Unplugged, Unfilter, etc) is an absolute joy to listen to. Very motivated team that exists by doing ads and using patreon. They prefer not to use ads and gladly take donation but I think they hit a nice balance.
My app of choice is Pocket Casts, works very well.
Oh, I also used to be a fan of Linux Outlaws, they had a fan made foss app that integrated with Indenti.ca (foss twitter clone based on status.net), you could automagically chat using a hashtag unique to the current episode. That was a nice experience and worth using the app for.