Memetics was influenced by him, since he coined the term, but it's hardly a "field" in the same sense as Computer Science!
In writing his book, Dawkins ignored the last 2000+ years of scholarship on the nature of ideas, and influenced a tiny group of academics who are completely isolated from any other form of philosophy.
The Journal of Memetics (which was the only one of its kind) ceased publishing in 2005.
Dawkins never wrote a book on memes. He wrote a book on evolution at the genetic level, The Selfish Gene. In it, he drew a comparison to genes that replicate themselves using organisms as a vehicle to ideas that replicate themselves using humans as a vehicle.
It was a throw-away comparison, not the point of the book. But, the term "meme" is a good meme, and it caught on.
The point isn't that he started a "field". The point is that Dawkins's ideas about selfish/cooperative genes (and the extensions of those ideas to the very idea of ideas themselves) have given rise to new directions in biology (and philosophy, in the case of memes).
Ever heard of a "meme"?
Dawkins has contributed plenty to his field, and he writes very accessible books.
That essay by him obviously doesn't criticize the entire field. He's just telling his readers to put up some nonsense filters before they start reading padded fluff.