When Blizzard released LoD the 800x600 resolution was entirely new, before that D2 Classic could only be played on 640x480, and I do remember reading a Q&A way back in the days during the 1.08 or 1.09 period where a guy from the development team mentioned that in order to increase the resolution they had to rework pretty much all of the existing textures to achieve that.
Meaning that just increasing a monitor's resolution or forcing the game's textures on a new resolution without actual "core" rework on them would just result in stretched textures rather than crispier and more detailed ones. If I'm not wrong. But that was a long time ago. Like one person mentioned already, it's not a 3D game so it had to be done differently, by the developers themselves.