Although there isn't much to lend itself to how the game is played other than reading the controls, I nevertheless had a good deal of fun with this rather cool idea.
You might consider a few User-Experience improvements if you intend to further develop this:
- Match each chef's T-shirt color to correspond to they button that triggers them, in addition to floating UI for each button above their heads (or nearby)
- Have the D-Pad food-selection UI bob up and down slightly to make it more obvious, and have the currently selected food wobble back and forth, or have the chef with a little speech bubble indicating the current selection.
- Have the X/B chefs display a bubble which indicates what they'll turn the food in front of them into, if they can, and a special symbol for when they're holding something they need to put down.
- Have each chef highlight the slot they perceive to be in front of them with their respective color, signalling where they will pick/place items.
Otherwise, this is really well put together for a 2-day jam, making excellent use of assets, complete with fitting music and sound, and a really neat and challenging mechanic. Great work! :D