It's difficult to help you without knowing more details, but what you describe sounds like the game is in windowed mode and your computer's resolution is equal to or lower than 1920*1080.
If the game has the same resolution as your screen, then you should play in full screen mode.
If you want to play in windowed mode, the resolution of the game must be lower than the resolution of your screen and not the same, because the edge of the window, as well as the windows bar, will take up space.