Well, color theory is a vast topic, especially when it comes to color reproduction and so on, but for UI design this is of lesser concern. However, basic stuff like the color wheel, complementary colors, perception of colors in terms of perceived contrast, "signaling" colors, knowledge of optical illusions etc. is pretty much 101 knowledge of anyone who wants to create really good designs. There are many traps you can fall into if you ignore this kind of knowledge. This goes even further with the entire field of cognitive psychology dealing with such things.

Typography also plays parts in human facing design, like being able to discern I and l and other such things. You may get by without all that, but I have seen too many cases of broken stuff, and that website from the OP is a big mess, pretty much counterexample of what I call "good design".