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You cannot fill the screen because the game is locked to a very low resolution. To my knowledge, there is nothing you can do to solve this.

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Same result. The game is physically locked to a very low game resolution, anything higher just causes the game to be surrounded in bars. Believe me I've tried and I have a 1920x1080 monitor myself ;)

You can probably change this stuff in your graphics settings. Yes, the game runs at a fixed, low resolution but you should still be able to get it to at least fill the entire vertical space of your monitor, if not the whole thing. Right-click on your desktop and select properties from the menu. Look for your graphics card settings. Once you've found them, look for scaling options. You want to enable scaling if it isn't already. There will also be an option for "preserve aspect ratio" or something similar. If that's checked then you'll get black bars on the sides of the screen, but the image will not be stretched. If you uncheck it then the image will stretch horizontally to fill your whole screen, but it will look distorted. Up to you which you prefer.