Do you mean this post?
The word "stakes" in the first sentence should probably read "establishing which of the things the player has staked is under threat in the particular moment of play".
What the player stakes is a combination of their immediate intent in the action declaration (intent + task), together with the build elements (Beliefs, Instincts, Relationships etc) that are threatened or put under pressure by the immediate situation the GM has framed.
Consider the example of my failed roll for Thurgon's search of Evard's tower for spellbooks. The GM chose to have, as the failure, the discovery of letters implying that Evard is Thurgon's maternal grandfather. He might have narrated something different, which put pressure on a different set of concerns that I have brought to the table with my build and play of Thurgon, like his place within and commitment to his military order (and this had indeed happened, earlier in the game, when the demon Thurgon fought outside Evard's tower seemed to be connected to some sort of dark secret or pact that had brought the order undone).
So the player brings the stakes, but the GM is the one who puts them under pressure by framing, and weaves them into consequences when checks are failed.