That chat is just StayDead musing on what he thinks the story might be based solely on what was revealed in the trailer, and wider knowledge of the Zelda timeline, and I think it's fairly clearly flagposted as that. I assure you this was recorded well before any story-related footage or info was available beyond the trailer itself.
It probably sounds worse now than it does when we were recording it because that info is now 'out there', so you'd be suspicious about fan theories and whether the fan theorist has heard something from a leak -- but it's clearly not info we had. We were just excited about the hints of story in the trailer and, as Zelda fans, wanted to discuss what some of those hints might mean to us.
Obviously don't listen if you don't want to but I think describing it as 'spoilers' is really stretching the term. I'm a bigger Zelda fan than you fact and I will fight you to prove it (etc), but even I think you have to be quite oversensitive to not want to hear this kind of fan discussion. Mostly because fan theories are almost always wrong -- at the end of the day if StayDead's 30 second off-the-cuff of 'do you think the story is going to head in this direction' was what they actually went with, they'd be paying StayDead to write the games rather than their expensive team of writers. I would be pretty disappointed if the story of this game was something that could be predicted by some guy on the GRcade Podcast.
Of course, if your media blackout extended to even the trailer, don't listen to the podcast. Again, I think that level of media blackout is a bit paranoid, but it's your call.
(I'm not responding because I'm trying to convince you to listen, I don't mind if any particular person chooses to listen or not, I'm just responding so other readers don't get the wrong idea.)
P.S. As Pedz immediately pointed out, StayDead's theory didn't even have a self-consistent internal logic.