The majority of the work was not really the changing of the screen resolution itself, but the updating of all the things in screen.
When resolution changes I have to update the background size, update GUI positions and scales and also make sure things keep their aspect ratio.
Next to all this I've implemented a working settings configuration file in which the set resolution is saved. All in all a lot of new stuff which is difficult to show you.
At least I can show you a gif of successfully changing between resolutions.
Next I'll keep working on the game settings. Fullscreen/windowed mode is up next.