Hello,
I am a very frequent Big Box user and this is an issue that I have only noticed since v10.3 and now in v10.4. Half the time everything still works perfectly. Half the time after quitting a game, Big Box will come back and hang with only the box art showing. The Big Box functionality isn't totally dead, you can hit enter and it will re-load the game you were just playing (since the most recently selected option was, of course, "Play Game"). I can hear the cursor moving up and down the invisible menu if I press the arrow keys. However you can't navigate away from the hung screen and I need to force quit Big Box, even if I knew exactly how to navigate to the quit blindly.
EDIT: After some more testing, it doesn't seem to work 100% right in any case. It seems like the problem falls into one of two buckets seemingly at random:
Case A detailed above
Case B: When a game is selected, Big Box starts to pull up the Game Details screen but also immediately launches the game. (Note: The Skip Game Details option is not, nor has ever been checked). Now when the game is quit there is no "Game Over" screen, but it exits fine back to the Game Details menu.
I can tell whether or not Big Box will break upon exiting a game by whether or not it correctly loads the Game Details screen before launching the game. Correct Game Details = Broken upon exiting. Skips Game Details = Okay upon exiting.