I have tried looking around for solutions to this problem and did find another thread, but nothing there solved the issue for me. Trying to launch the game normally through GOG does the exact same. I have attached a screenshot as well so you can see what it looks like exactly.

I have messed around with a lot of different of options in HD+ but none of them seemed to change anything. Any help would be greatly appreciated.

I get perfect results with these settings:
Mode: 32-bit True (stretchable) GDI
Source size: 800x600
Stretch Filter: Bilenear SharperX2

And these boxes checked:
HD+
System Cursors
Full Screen Mode
Ni CD/DVD

If that doesn't work, you probably need to change the setting for your video card.

The source size is what did the trick. 800x600 wasn't in the drop down menu but typing it manually worked, thanks for your help!

You can go pretty wild with the "source size" values, no matter if they are included in the predefined values

For example, if you want to keep the original aspect ratio, you can also try something like 1200x900 (1.5x the original resolution), which will give a larger field, and the text is still pretty readable.... if you happen to have a vertical monitor you can also go nuts with 900x1200 or whatever

On my standard 1080p monitor I personally like one of the presets at 1365x768 source size and

Mode: (stretchable) 32-bit OpenGl by Verok
Stretch Filter: None + Lanczos