Really impressive project. You definitely went above and beyond on this one. The formatting looks consistent and the game is coded really well. Checkers is a very difficult game to take on but you nailed it. The extra features (vs computer and multiplayer) are awesome.
The only thing I would suggest is to use addEventListener over adding functions to the oninput and onchange of your elements. The reason for this is that with addEventListener you have a bit more control over propagation if you need it at anytime during the development of the game. This is due to the 3rd argument on the method which you can read more about in the docs if you're interested. With that being said there is absolutely nothing wrong with the approach you took.
Well done and keep up the good work.