There are tabs. One of the tabs is your current game.
If you hover your mouse over the tab, an "x" will appear to close that tab.
Chess.com should change the way that feature works. It shouldn't be a hover-over to find the "x". It took me a long time to figure it out also. I actually had to ask someone how to do it while following a GM.
You can clean the board.
In the old software, I could clear the board after a game. But in the new version, I am not able to see a clear button. The last game remains till the new game start. If I have lost the last game, I would definitely like to wipe it off the screen!!!