Turing's theory was formulated in an era when physics and chemistry were the foundation components of biology. The problem he was trying to solve is: How is biological complexity achieved in terms of fundamental chemistry and physics? At the time, chemistry could explain how two poisonous chemicals, sodium and chlorine, could combine to produce a substance as benign as common table sale (NaCl). But nothing could explain how a single cell could develop into something as complex as a fish, or a mouse, or a human being.
In 1953, Crick and Watson published a paper in Nature that revealed the chemical structure of DNA. The discovery was a revolution in science because it changed biology from an amalgam of physics and chemistry into an information science. In DNA and RNA, a whole vocabulary of computing was encoded. Suddenly, the complexity of biological processes such as embryogenesis, heredity, and cancer could be understood in programmatic terms through the molecular language of DNA.
Turing's theory of chemical morphogenesis doesn't mention DNA. As such, it is too simple to explain morphogenesis per se. Rather, his concept of intercellular reaction-diffusion may be applied to cell biology inter alia, but it isn't the big picture. Crick and Watson worked that out, thanks in no small part to Rosalind Franklin and Maurice Wilkins.