The problem is that Dark Souls does not support resolutions other than 1280x720. Even though the game lets you choose another resolution, it will simply scale the image to fit the resolution.
I tried ticking the option 'Full-screen' in the scaling mode and nothing happened also.
There's two (possible) reasons for that:
Since the game is already scaling from 1280x720 to 1280x1024, your GPU no longer has to do any scaling. You should try configuring Dark Souls to run in 1280x720 and setting the scaling behavior of your GPU to "Full-screen" instead of "Aspect ratio".
You left the "Perform scaling on" option to "Display" instead of setting it to "GPU". Your GPU will tell the display to use "Full-screen" scaling, but there's no guarantee your screen will do it. If changing the game's resolution to 1280x720 doesn't work, try to switch to GPU scaling.
As for YouTube, the scaling here is controlled by your browser, which is not configurable (I do not know a single browser that allows configuring scaling behavior).
To fix that, you could try and enable the "Override the scaling mode set by games and programs" option in Nvidia Control Panel (just below the "Perform scaling on" option), although there is no guarantee it will work for all games or programs. For instance, I doubt it will work with Dark Souls, but it might work with your browser. It's worth a try.
If nothing works, buying a 16:9 screen (such as a 1920x1080 screen) will fix this issue for pretty much all games released after 2007. You will still have problems with many movies and some YouTube videos.
A lot of movies (especially those from Hollywood) were made in the 21:9 format and will have black bars even on a 16:9 screen. Also, YouTube videos made by smartphone are often shot in portrait mode, so the aspect ratio will be 9:16 instead of 16:9. This means the black bars will be on the left and right, instead of the top and bottom.
Unfortunately, without full-screen scaling, black bars are inevitable.
