Hello. I have been working on a chess- and platformer-based quest game for 7 years, which is currently called Chess Quest. It wasn't until recently that I continued working on the game. Now let's start on the question...

I have set up a room where playable chess pieces are capturing opposing chess pieces. However, this room does not look like a regular chess board; instead it resembles that of a normal video/computer game, especially that of a 2D platformer game with characters and chess pieces. The problem is that I am not sure how to make it function like an actual chess game (with levels more complex than those of chessboards).

Can anyone tell me how to make the players move like chess pieces? Thanks for reading.

Maybe have the player only able to move if he has certain objects (hats) worn/held : e.g. Crown (King), Tiara (Queen), Helmet (Knight), Robe (Bishop), Armour or Shield held (castle), Cannon ball held(Pawn) or more creative alternatives!

The illusion of being in a single room could actually be a multiple set of rooms with descriptions to fool the player into thinking he is still in the same room?

For chess related moves on a grid, instead of using the "n" "s" "e" "w" (etc) existing single commands of movement, make new commands that will move you to rooms further away in 1 single command : e.g. (QUEEN) "nnnnnnnnnn" for a long move straight 10 rooms away instantly.
CASTLE :"nnnnn" moves you 5 rooms north instantly
BISHOP: "enenen"(effectively a diagonal) moves you to the correct room permitted to move to.
KNIGHT :"wwnnn"

Maybe lock all movement from room to room unless unlock to room via conditions (stuff worn/held).

So you could have a full chess board grid of rooms or a more interesting version of chess with layers. All movement could be interesting and limited by what objects you reveal and allow player to have, wear or hold and use to move!

Good luck. Sounds like a massive interesting project.

@iantommo
Nice idea, but my additions are more significant than other forms of chess. I already have 6 new chess pieces added aside from the modern chess game (tyro, warden, noble, baron, baroness, and a new spirit named the Kingsprite). Not only that, but there are characters that can challenge or talk to you. Like many platformer games, there are special powerups and platforms such as the Extra Rook which geminates, or doubles, a rook (similar to that of the extra spaceship in Galaga).
So moving my pieces can be a lot of work if you make a complex room.