There is a limitation of the Mac OS X component that CrossOver uses (quartz-wm, to be specific) such that a window that is created with a title bar can not be converted to a window without a title bar. Some games create a new window when they switch from windowed mode to full-screen, which works fine. Other games, however, try to convert the normal window (with a title bar) to a full-screen window. The result is what you see -- a full-screen window with a title bar, which is a mess.
If you can configure the game to go directly into full-screen mode without ever creating a normal window, then you can avoid the problem.
To get the effect you see in the screenshots, you can use the Restore Display item in CrossOver's Window menu. Since the menu isn't accessible in full-screen mode, you invoke it using its keyboard shortcut Command-Option-R. That forces CrossOver out of full-screen mode. The game continues to run in the window it had been using, but the display is no longer captured, so you can see the desktop and access other applications (Note, though, that some games react really badly to losing focus unexpectedly.)