>>96008202
NTA, but I can try to answer that. In-game, the DM is represented as an actual GMPC that's basically a Dragon Guide, or a spirit that watches and records the player character's journey. Essentially like Gandalf if someone slapped his staff out of his hands, gave him a lute, and told him he's now the party's Bard. It basically gives the GM the chance to do minor things like give players an mulligan on bad rolls, or give them a minor benefit for doing something suited to their adventure. Ex.

>The Tale of Nostalgia
>If the PCs roleplay having nostalgia for home, they can ignore all negative effects of mind-based status effects for the rest of the session; this affects up to two PCs at once if they meet the conditions.

Note that the game says the Ryuujin's presence is explicitly optional, their capacity to use their powers is heavily limited, and emphasizes that the game's focus should always be on the player characters and not what the Ryuujin is doing for them. But yeah, that's what I believe it means when they say the DM is affecting the "story", since in this case it's the storyteller effectively nudging the dice once or twice to make the gameplay portion more fun for the players if they choose so.