I'm not sure if people have done this before reportedly, but I did find a solution that worked, at least for me.
(For context, I'm using Windows 7)
So first I opened the control panel and clicked on 'locate and fix problems' (I don't know what it's called exactly in English versions).
Then I clicked on 'Find problems related to the processing power', or again, whatever it's translated to/from.
In the troubleshooting process I was given the option to prevent some kind of rundll program from starting on launch, and I decided to do so.
I can't really provide details regarding that, since I can't redo or backtrack the troubleshooting again as it considers the problem solved.
Afterwards Hammerwatch didn't crash anymore, but it reduced the screen to a limited amount of colors, and as a result everything looked dithered and every icon was from a decade-or-more-older version of Windows.
To fix this, I opened the properties-window for the Hammerwatch.exe file and opened the 'compatibility mode' tab.
There was a checked box, which said the application is opened in compatibility mode with Win7 being the target version.
I only had to uncheck the 'restrict to 256 screen colors' box and then the game ran all fine.
I sure hope this is a fix that everyone can use, since this problem had been reported already in 2014, and I never found a solution for it.