As far as the image is concerned, it looks like you have some ghost reflections in the second render. In the bottom right corner, it looks like there are 6 pieces that are just floating out in the middle of nowhere, but we can’t see any corresponding pieces.
There also appear to be some jaggies between the chess pieces and the wall in the background, most likely because the z-depth pass doesn’t get anti-aliased. Try enabling Full Sample under Anti-Aliasing in the render properties. It’ll take longer to render but should fix that up a bit.
As for the game, it’s not as much of a problem for a game in progress like the second render, but when you’re starting a new game like in the first one, the queens should be on their own colors so that they’re directly across from each other. Also, based on the way you modeled the shapes, it looks like you put the bishops in the corners when they should start right beside the king and queen. Just swap those and you should be fine.
Besides that, I like the style of the pieces and the board, and you’re on the way to a good render once you get those issues fixed.