Sure, probably. As per the reference sheet for the rules/laws of dialectical materialism: https://en.prolewiki.org/wiki/Library:Elementary_principles_of_philosophy#The_laws_of_dialectics

As a mnemonic:

1. Unity & Struggle of Opposites (The Engine)
2. Quantity into Quality (The Leap)
3. Negation of the Negation (The Spiral)
4. Primacy of Matter (The Substance)
5. Social Being Determines Consciousness (The Method)

You have a unity of opposites between the two players and their armies. Neither white nor black can exist without the other (it's not a game of chess if there's only one side in it), but they are diametrically opposed - by definition the existence of one must be ended. This is not a rule of diamat by itself (that one must be destroyed), just that you have to resolve the contradiction somehow, and as long as even one black or white piece remains, the contradiction will continue to exist (excluding checkmate rules and other 'no more than 5 of the same movement consecutively rules to break locked states at the end-game).

Maybe this is where Clausewitz's conception of war also plays a part (he was resolutely dialectical, not materialist though). He views war as a duel on a large scale - also showing that we go from the particular to the totality. When pawn takes pawn, you resolve the contradiction of the duel (pawn against pawn, where both players can equally take the other's pawn if they decide to) by making your move and capturing the pawn. But this creates further contradictions, either in your possible moves or the adversary's.

Quantitative change leads to qualitative change and vice versa. You can see this on different levels, taking enough pieces lets you win the game (qualitative). You can also see it in the 'duel' - if you secure a nice position with say bishop and knight threatening a single piece, then you have a quantitative difference which makes the capture pretty sure on the next move (take with knight and knight will be protected by bishop). You accumulate (in most cases) quantitative change until it leads to qualitative change (excluding that sometimes people just miss the obvious and expose their king in like turn 3 or 4).

The negation of the negation means that, well, the negation contains its own negation. For example the bourgeoisie was the negation to the aristocracy, but the bourgeoisie created its own negation in the proletariat. It is "contained" within the negation. Moving a piece is usually done to put you in a favorable position but can also expose you. Taking a piece may lead to your own piece being taken right away in the next turn. You might give a bishop to a pawn so that the pawn moves, negating the king's safety in the process and leaving him exposed.

And of course materially speaking you have to play the board you are given with the rules of chess (rules being more akin to laws which are part of the superstructure which diamat does not discard). Moves act in the material world but only the moment they are actually carried out -- you may plan 50 moves in advance in your head, but if the adversary makes a move that wasn't in your calculations, all of that planning did not materialize and you are forced to change your plans.

The way we play chess today is itself inherited from the centuries of social labor of previous players who advanced and perfected strategies. The default opening used to be pawns in the center for decades, but was replaced in the 1920s by the fianchettoed Bishops. This was a direct negation of the classical doctrine of occupying the center with pawns.

This is a brief overview, the important points however are:

1. To look at it in its totality, not in its particular. It is not enough to look at a duel (pawn vs pawn) and make broad sweeping rules, just like the laws of dialectics are not a checklist that you compare to. This was just a quick starting base.
2. This is because diamat is a living science meant to change the world and not just analyze it.

Whether you could use these rules to perfect your game of chess, I'm not sure. I think over the centuries players have basically perfected strategies, which are themselves a material reflection. If we hold that diamat is the objective truth of the universe, then it makes sense that eventually some principles will be reached without people necessarily knowing about diamat.

In what sense? Chess has it's set of defined rules and turns so i don't see how you could "apply diamat". However it can help you getting better at chess or at anything really.

yes but the method changes in which the superstructure becomes a primary determining factor and the base is in which determines the possibility of success and diamat would be difficult to utilise beyond descriptive potentials as you have largely detached yourself from a generalised predictive reality into an individualized and easily malleable one

The more players you have the more effective strategizing becomes with diamat

Since diamat isn't really tied to ideology or morality on it's own it just acts as your preferred analysis method so it isn't actually that special

No, games aren’t based on reality (the material).