Aaah it's so good, I wish i'd thought of it.
Ok I will explain it a little bit.
I think the menu's amazing with all these cryptic icons but obviously it's going to throw some people. Just bear in mind that all the symbols actually mean a thing and you're meant to understand them and you'll be fine, you only run into problems if you stop expecting things to make sense.
The game is set up like a usual chessboard, 1-3 rows of pieces on each side. Players take turns picking a piece to move and moving it. The piece identities (both rules and icons) are randomised each time you play, but each player has the same set. There is no reference for what pieces do - you have to select one to see its available moves and then you're committed to moving it even if none of those moves are good for you. The goal is to kill a certain number of your opponent's pieces, counted by boxes along the edge of the screen. Some pieces are "royal" and are tinted a different colour, these count for 4 kills. (I took quite a while to figure out the win condition as i didn't notice the score boxes at first and the game often ends when taking a royal piece anyway.) When a piece reaches the far edge it has the option to teleport back to its start position (perhaps slightly inelegant but it stops pieces getting stuck if they only have forward moves).
And that's basically it.
The pieces aren't completely random. Typically the front row consists of "pawns" with movement limited to 1-2 spaces away and back rows have the stronger pieces which can move in rays across the board, knight-Ls, and more unfamiliar patterns. So despite initial impressions the game actually isn't very chaotic, there's a clear pacing as you develop your position and bring the stronger pieces into play.
You can take your own pieces. This is rarely desirable, but sometimes you are forced to by having selected a piece which has no other moves available. Don't blame the game for this. Picking an unknown piece without many freedoms is a known risk, usually you can avoid this if you think about it. And for your first move, all the pawns are guaranteed to have a safe move available (although opening with a back row piece is an interesting possibility - you'll probably have to take one of your own pieces but you might gain tempo?).
I'm worried the inclusion of an AI opponent will hurt Chesh, it's very much a game for playing against a human. I don't know to what degree the AI models "knowledge", I hope it does only use information about the pieces that it's "seen" - but that's the point, I don't know, I can't trust it. Whereas playing against another person, I know they've only seen what I've seen so I can trust them to provide a fair contest. Anything they know that I don't is something I could have known if I'd thought harder, remembered better. It's great. But I worry a lot of people will start by trying this with the AI and then since that version of the game is not as good as playing against a person they will give up and never enter that battle of wits. This is something I felt happened with Glitch Tank, a game similarly reliant on human limitations. So please try it out against a friend. (It has online play, hopefully that will help but if there aren't enough players long waits for an opponent may discourage people from trying.)
I like that even once a piece has moved its full capacities might not be revealed. You've seen it move forwards, but its backwards movements may be different. You've seen it move one step east to capture, but you don't know if that was its maximum movement or if it could have moved further had there not been another piece there.
I really like how moving a piece reveals information to both players. Sometimes you will avoid using a piece in order to hide its properties from your opponent - make them pay the cost of revealing it. I like to threaten royals before they've been moved, gambling that they might not have a way out. In general Chesh allows for aggressive strategies that would be impossible in Chess: you can risk exposing yourself because your opponent might not know they can take you or which piece they can do it with.
There end up being really interesting mind-games in terms of what you each know about the pieces, and what you each know about what the other knows. You've seen the same information but under pressure you don't remember all of it. Sometimes you can deduce that your opponent has forgotten what a certain piece does, and take advantage of that. If a piece was moved early on and not since, it's likely been forgotten. But that leaves another level (which I haven't reached yet) where you might bluff having forgotten something. Sometimes you can bluff just by moving a piece very confidently into danger, hoping your opponent will trust that you know what you're doing and not notice that they can take it.
There's a lot of skill in managing your memory. You can't remember everything so you have to pick what is most important to keep hold of. If a piece has very powerful long-range moves, it's a priority to remember that over something weaker and more local. But sometimes remembering the exact movement of a minor pawn can be critical - that one can attack any adjacent square except the one directly in front of it so that's where I'll move. And especially remembering something your opponent doesn't is advantageous, whatever it is. People are more likely to remember pieces that they've moved themselves, you can use that. You develop a weird internal language to remember approximately what pieces do and build mnemonic descriptions to connect them to the icons - the gravestone's a forward-knight, side-flower has ears, dog machine fat bishop. Sometimes the position of a piece on the board is enough to encode its movement, you can see it's a pawn and that you moved it diagonally because it couldn't go forward, so you don't need to store that in memory right now.
Ahh Chesh. It's really good play it.
(Disclaimer: I playtested Chesh and drew some of the icons for pieces.)