Theoretically, shouldn't analysis of any chess move have exactly nine possibilities? 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.
You are somewhat correct. In theory, each position can be correctly categorized in one of three ways -- win for the side to move, loss for the side to move, draw, all presuming "best play" by both sides from that position. That last caveat is required to make the ideas of "will win", "will lose", and "will draw" well-defined. But that caveat also means that the side to move can never improve on the position categorization, because that categorization already presumes (prices-in) that the side to move will make its best move. So the only possibilities for move categorizations are: (W,W), (W,D), (W,L), (D,D), (D,L), (L,L). I.e. six instead of nine. The side to move can only hold or worsen (blunder) its theoretical value, in other words.

As for severity of error, presumably (W,L) is worse than (W,D), but other than that, blunder is blunder, yes ((W,D), (D,L)). And any move that maintains value is a theoretical non-blunder, yes ((W,W), (D,D), (L,L)).

As to engine scores, they are in most cases theoretically "meaningless" I suppose, as above, but not objectively so. They could be considered to be trying to estimate the probability that the theoretical value is closer to W, D, or L, on some scale, given the data they have been able to glean so far in their forward position search. And sometimes they do produce theoretical values (forced-mate detections). But I've also got to think that the error-bars on non-theoretical engine values are also pretty large, meaning that we're talking about estimates of estimates of probabilities, which is pretty, well, non-definitive...

Also, see Saibot's answer regarding so-called Tablebases. Chess has been solved theoretically for all positions with 7 or fewer pieces on the board (two kings plus up to any five pieces). Here is an online resource for most of the 6-piece tablebases: http://www.k4it.de/?topic=egtb&amp;lang=en

Another wrinkle on theoretical categorizations is "distance to mate" for W and L positions. Presumably a win in fewer moves is theoretically "better", so a (W,W) move that doesn't reduce "distance to mate" could be considered a "blunder" as well, as could a (L,L) move that shortens "distance to mate".