Since chess is finite and deterministic, it is theoretically possible to objectively label any position as winning, losing, or drawn. For example, it seems very likely that the starting position is drawn.
Therefore, the current system of "score" that engines use to analyze a position is actually nonsense from an objective point of view. With enough depth, the "score" would always be +100 (or whatever the engine uses for forced checkmate for white), 0 (drawn), or -100 (forced checkmate for black). Are these not the only possible evaluations of a position?
If so, it follows that moves can be characterized in exactly 9 ways. If W, L, D represent won, lost, and drawn positions, the nine possibilities can simply be written as ordered pairs of game states before and after the move.
For example, a move that makes a won position into a drawn won could be (W,D).
Our intuition of a range of severity for mistakes is something that a theoretical supercomputer would not share. Is it then meaningless to speak of how bad a mistake is? It seems to me that the only relevant point is whether it changes if the game is objectively won/lost/drawn.