There's a key you have to press to make the graphics in DK go from this low rez, pixel city crud to something better, but for the life of me I can't remember what it is. I had the same issue even back when it was released. It still looks fine on my 23" monitor today. imo. Altho I always played zoomed out all the way, never all in close, and if you were using DosBox or something, I can't speak to how it works using that.
You can download DK FX mod, which gives support for widescreen resolutions.
Also I love, love, love Dungeon Keeper. It's a shame though that Deeper Dungeons expansion pack isn't included in the gog's release.