pressing the power button the monitor exits the game and returns to the desktop

What is the model PC that you have, is it a laptop or a d desktop,. What I do if I want to leave a game, I do nothing and pause the game and let the PC go to sleep, as "able to leave the screen off while it is running in the background" in a game, the system will go to sleep and turn the screen off automatically if you have the sleep and screen off settings set appropriately, as whenever you come back to it you wiggle the mouse and the game should come back to where you left it. Try that as any time you press the power key the game will either go back to the game's settings or in your case it crashes as probably this game must not be fully compatible with your PC and that is why its happening, as there is nothing wrong with your PC if the game is playing as this symptom happens all the time. Also try to make sure that you are running the latest OS updates and drivers and graphics drivers.

Likely the game is seeing that it's display went away when Windows did the refresh caused by the monitor change.