I don't think it does. The concept of the dungeon might be something like "Old gatehouse being used by the local goblin tribe as a secure lair." This serves the purpose of guiding the expectations of the GM and players in terms of its layout and likely general content. The island concept in Agon is, if I understand the game correctly, a thematic thing, like "a place where kin strife has lead to an endless cycle of revenge" or something like that (
@pemerton may quibble with this, I'm not sure what the Agon designers have said in terms of a really good island concept).
Which shows the great differences between these games. Agon is about the PC's relationships with these gods and what they represent (and I assume that also represents their self-conceptions to a degree at least). D&D is about loot and XP. There COULD be maps and such to give clues about the nature of treasure in the dungeon, etc. but it won't bear on the nature of the characters, that's already decided!
There might be SOME similarities, but the 'landscape' being populated is pretty different. "A grieving mother bent on revenge for the death of her son" is probably not a whole lot like "a goblin burglar who hopes to get a chance to steal some of the party's treasure by pretending to ally with them." (and that later is about at the upper limit of what I've seen in classic D&D for that sort of an NPC).
Well, in some very high level sense, yes. That is both systems require some sort of dramatic opposition in order to make something interesting happen. In the case of the dungeon it would be pretty blah to just have treasure lying around and no danger to overcome. In the case of Agon the strife and trials are, IMHO, the 'meat' on the bones of the story. Someone has to convince the kin to stop strifing with each other and make peace, and this is going to require achieving a number of goals set by the GM. Also, POTENTIALLY at least, this might be somewhat dynamic. That is, play might reveal some different and unanticipated narrative that might change the trials to a degree (again, not actually familiar with the Agon rules and how or if that is handled/envisaged).
Well, D&D is VERY specific about how and when things are determined! When I search for secret doors, a certain die is rolled (d6 IIRC in basic D&D, though I'm sure that is not always the case) and if certain numbers come up, and if the GM placed a secret door in that location, then the GM MUST SAY "you find the secret door." And if there isn't one, then he must say "you find nothing." Now, it sounds like in Agon a mystery might be something like "who is responsible for the death of Marco?" It sounds like the GM will have the answer to this secret and simply reveal it when its dramatically relevant (IE as part of some scene where the PCs attempt to resolve whatever strife this death is causing). Honestly, it may even be more different than that, as in many narrative type systems these sorts of things are not given specific answers until someone takes actions that would reveal such an answer, but I am not 100% sure how Agon handles that.
I expect that the nature of the rewards in a game like Agon is pretty different. D&D rewards are canonically XP, loot (which in many versions of D&D also determines XP, making loot THE goal), and possibly intangibles like alliances and such (though these are typically not really prepped beforehand, but usually arise out of RP during play). I have little idea what the rewards are in Agon, but my guess is they are more along the lines of favor with certain gods, maybe some sort of XP or other currency, etc. Wealth or some sort of magic might also be options, I don't know. I would agree that there is SOME overlap, rewards is rewards it's kind on the label! However I expect the main goals in Agon revolve around the actual playing through of the issues on the islands and how that process is reflected in changes to the internal life of the character. No such internal life is either assumed or required to even exist in D&D, you can happily play in pure pawn stance.
There are parallels, undoubtedly. I think, however, it is in the differences that we find the heart of each game, not the similarities. Again I am not familiar enough in detail with Agon to know exactly how the mechanics of the game, and its process of play, mesh with the prep and how it contrasts in all respects with classic D&D, but given what I know about narrative systems that are said to be in the same general family, I think the play experience and how the prep manifests, will be quite different. As I said a while back, a horse cart and a porche are both vehicles, and can do some of the same 'stuff', but you can only take that similarity so far. If you try to drive your porche through a plowed field, you will find out real quick it ain't no horse cart!