I can't seem to get a higher resolution than 320x200, even though I edited the Dosbox confguration as explained by @PhilsComputerLab and the mentioned YouTube video.

What am I doing wrong?

Never mind, as I understand that IS the game resolution ...

Use any other video output than surface to get fullscreen, but game render resolution stays 320x200 wether you upscale it or not.
You can try out some shaders though.