This assertion has always been strange to me. This American Life was releasing their episodes as podcasts for something like 7 years before they decided to do Serial. Shows like Adam Corolla, WTF with Marc Maron, the BS Report, Joe Rogan Experience, etc were all very successful before Serial. Major media companies like NPR, CBC, BBC were releasing podcasts and dedicated podcast companies like TWiT.tv had existed for years. I think you can kind of credit Serial for popularizing true crime podcasts but it gets way too much credit for the success for the medium.
In fairness I think Bill Simmons, Joe Rogan, Marc Maron and Adam Carolla have had their praise for moving podcasts along. Same with This American Life.
Serial was different, though in that it was a multi episode look at something. This American life had segments and still had to be designed with the radio listener in mind - who was probably only in the car for 30 min. I don't think Serial is that uniquely good - but it was different. We just are kinda dumb for having all of "podcasts" under one term instead of a bunch of genre terms.
You could also just call them “radio shows”. It’s a weird thing that the company that made iPods for a few years defined that term and we have gone with it since.
As for the earlier part of your comment - it’s there in the name, “serial”. That was the experiment. But there have been serialized radio shows back when radio was the leading medium. We just don’t remember that time.
What I think is key here is that these people had formal experience and mentorship in doing radio. Lots of it. To them it was just applying that expertise to something we call something different due to shifts in distribution tech.
Serial didn't create the demand for podcasts — that had already existed, as you say — but it proved out that demand, in a way that made advertisers take notice; made it possible to commercialize podcasting; and so led to an explosion in the number of podcasts, because it was now a predictable media business model that the stodgier kinds of investor could get behind.
I listened to at least one proto-podcast back in the pre-iPod era of the late 90s: Pointless Audio with Kevin Pereira. It's still available in some form: https://youtu.be/XXqxUAzt6u4