I've been having this issue for a while as well, every other clickable part of that dialog box works. Game Review, New match, Rematch, even the type of result, that all works. It's just the X in the top right doesn't function.
Strangely, on the occasion I'm able to click the X before the Game Analysis has completed/loaded, it DOES close the dialog box. Once the Game Analysis results come up, the dialog box expands slightly, and the X moves upward from where it was, so maybe that's got something to do with it.
Recently I have been experiencing a problem in which if I click new game button on the pop-up window a new game starts with a pop-up of draw.... I can't even close the window and game just resigns. I have lost countless games due to this and chess.com has banned me for sportsmanship policy please help!!