All fly fishers have their favorites, but I think most would agree that's a pretty solid starting list.
Here would be my suggested changes to the list:
To simplify even more, I think a beginner could drop the Griffiths Gnat. Most beginners won't be fishing the small midges.
Also, instead of Adams, I suggest the Parachute Adams. Both are good, but I think the Parachute Adams is better. Because parachute style dry flies work well in both flat, slow water, and in fast, broken water.
Also, in some of the dry fly patterns such as Adams, Sulphur, and Elk Hair Caddis, he's suggesting sizes 10 -18. While it's good to have a wide range of sizes, concentrate more on the mid range, i.e. the 12, 14, and 16 sizes. And especially sizes 14 and 16. Because that is what you will actually be using the most.