I'm not sure I understand what you mean when you say that "biology is much, much shallower". Shallower than what, and in what way? What might it look like if it were deeper?
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".
And, just to finish off, the machine is stochastically nondeterministic.
And this is a personal feeling, but there is less encapsulation, in biology. There are less 'categories' of things that build on top of each other that you have to learn, but those categories are immense and the knowledge in each of those is incomplete. I suppose you could say the knowledge in some of programming is 'incomplete' by virtue of closed-source encapsulation (trust us, this hardware works like you think it does), but that is somewhat artificial.
This is what I came up with in a hurry for biology:
...elements
atoms
chemicals
nucleic acids
genetic circuitry
peptides
proteins
multiprotein complexes
microcompartments
organelles
cells
clusters of differentiation
organs
organisms
communities...
Without knowing how much more there is to know about biology, how can we expect to see certain features or not? What about tasks that are supremely efficient in biology but resource intensive "in silico"? I'm having a hard time fathoming biology as shallow in any way. The fact that it's bootstrapped and live, that you don't get to restart the computer or cut the flow of information makes it all the less shallow to me, unless I'm misunderstanding how that word was used.