De Jong being a DM is pretty much tied to the fact that at the DM you play exactly in the middle of the pitch, in all directions.
If you check the positional map of players, the one player who has access to the most teammates in terms of triangles is the defensive midfielder, or in our case the deep lying playmaker, because that is what De Jong will be to us most of the time considering our possession game.
In the rigid setup of Valverde, the wide midfielders don't have very often access to each other. If you check the pass maps during Valverde, you'll notice that the two vertical halves of the field do not have very often passing connections to each other because there is low fluidity.
As a wide midfielder (either side of the central midfielder, be it RM, or LM) under Valverde the most used pass scenario is to fullback. That is basically wasting the potential of De Jong.