Peggle Nights, like all other Peggle games (that aren't Peggle 2), display at a 4:3 aspect ratio by default, with no way to change it. But on some monitors, it won't display like this, instead filling the screen or displaying in a 16:9 aspect ratio.

Since when I had this problem it took me far longer than I'll admit to figure how to fix this, this short guide should help you fix the issue so you can play Peggle the way it was meant to be played.

1. Open your monitor settings. Usually this is accessed via buttons on the monitor itself.
   
2. Navigate to a section which contains Display Settings (where this is located will differ from monitor to monitor).
   
3. Find and select "Aspect Ratio" (again, the precise location may differ).
   
4. Change to "4:3".

And you're done! You should be able to change your aspect ratio back to normal via the same method.

If you have an NVIDIA graphics card or graphics drivers, you should have access to an application called NVIDIA Control Panel. It can be used to potentially fix the aspect ratio permanently.

1. Open NVIDIA Control Panel
   
2. In the left pane, click on "Display" and then "Adjust desktop size and position"
   
3. Underneath "Perform Scaling On", select "GPU".

And you're done! If the issue still persists, try checking the "Override the scaling mode set by games and programs" checkbox below the "Perform Scaling On" menu.
If the issue still persists after this, try the Monitor Method above.

Big thank you to user -agent, from this discussion post for making me aware of this solution!