When you click the X on a Play game tab, it means you want to abandon the game. You will then see the Abandon current game dialog above. If you choose the Keep playing button you can resume playing the current game as if the X was not clicked.
If you wish to Abandon the game you first need to decide how you want the game abandoned. Here are the options:
HIARCS Chess Explorer examines the current position and makes the default selection the one it expects you will want to make
Choose the appropriate game outcome/action and click the Abandon button to abandon the game.