I click on a chess table, and the option is there to “Play Chess”, but when I click on “Play Chess” it does not go into the command line at the top. This happens with other things like “Pumping Iron”, and the guitar disappears when they pick it up to play.

Free to download or a commercial one.
Don’t care about fancy things such as 3D perspective. Just a flat bord image will be fine.
Give the reasons why you consider it is good for learning and improving game strategies, please.

I do. I belong to a chess organization in which I bring pizza to school and everybody gives me pointers on how to improve my game.