It seems that the default resolution for apps is only 1920x1080 pixel. I wasn't able to find more about changing the resoultion to 3840x2160, after all it is supposed to be a 4k SmartTV.
Modifiying http://tizen.org/feature/screen.size.normal.1080.1920 to http://tizen.org/feature/screen.size.normal.2160.3840 only scaled the application down, with the same crappy resolution.
http://developer.samsung.com/tv/develop/guides/fundamentals/application-resolution/