Ok for anyone else having this issue I kinda fixed it. It seems that the issue was partly due to outdated AMD graphics drivers/faulty DirectX files. After noticing issues in other games too, mainly League of Legends (the game would shut down with error message "DirectX error"), I decided to download the latest AMD Catalyst Control Center as well as the latest DirectX version. This fixed both my LoL error and the graphical errors in Rimworld.
One important thing to note is that if I alt-tab out of the game the graphical errors pop up again. It's a bit annoying, but playing in windowed mode prevents this issue completely in my experience so far. I do think that this is a compatibility issue with the graphic card or something though.
TL;DR: Fixed by updating DirectX and drivers for AMD Radeon HD 5700. Issue pops up if alt-tabbing out of fullscreen. Play in windowed mode to avoid problems.
One important thing to note is that if I alt-tab out of the game the graphical errors pop up again. It's a bit annoying, but playing in windowed mode prevents this issue completely in my experience so far. I do think that this is a compatibility issue with the graphic card or something though.
TL;DR: Fixed by updating DirectX and drivers for AMD Radeon HD 5700. Issue pops up if alt-tabbing out of fullscreen. Play in windowed mode to avoid problems.