DNA is like a programming language for a biological computer, a living cell. However, we don't know nearly everything there is to know about a living cell. We can't predict its mechanisms. There is no debugger. The compiler didn't come with an instruction manual. The code bootstraps itself into its own machine and runs in an environment we can't predict. And the syntax has been obfuscated and optimized by a genetic algorithm that's been running in parallel on quintillions of cores for a billion years.
Because the code executes on an unknown machine in an unpredictable physical environment, many features we might expect to see in a programming language are missing. This might be what he meant by "shallow".