That's one scenario where Task Manager can't kill a process. When a full screen game hangs, the graphic mode stuck as well. No amount of Ctr-Shift-Esc or Ctr-Alt-Del will bring Task Manager on to kill the process.
Switching to another virtual desktop (Win+Tab) can help if the graphics driver is still working normally. If the driver crashed, you have to wait for TDR to kick in and restart the driver (usually ~5s). That is, if it's able to recover.
When Task Manager is the active window you can control it with the arrow keys and view it with alt+tab. Typically the game has “Not Responding” next to it so it’s easy to select and kill using the delete key.