You are making a huge philosophically fallacious leap when you compare how we are able to study DNA sequence as information technology to assume that DNA sequences most be intentionally coded by a being in the way software is coded.
We rationalize things in terms of information - that is our common denominator of understanding, thus our brain tends to understand all things of the world in terms of information - whether it was human created information or naturally observed.
Dawkins does a great job explaining things to lay audiences. People understand the analogy, and I agree it is a good analogy and helpful in understanding the field of genetics.
Here is an actual real example of what your cells make from DNA.
https://en.m.wikipedia.org/wiki/G_protein
This is what a protein molecule your DNA makes looks like (structurally). Apart from replicating itself with the assistance of other chemicals, that is all it does - it makes things like that (via transcription through RNA). Now what those proteins do are quite important to our lives as human beings.
Those proteins have chemically reactive sites that bind to various other chemicals inside and outside of the cell and influence the behavior of the cell (and your experiences as a human being). It turns out the random-ass order of those amino acids effect the bond angles and internal stresses of that protein chain and make it form weird-ass shapes. Those random weird shapes effect which bonding sites are exposed to chemicals in your body (things we call neurotransmitters because we like to think of things as information), and the interaction of those chemicals on those bond sites can further affect the distortion of that protein’s natural shape, exposing other body sites which induces other physiological effects you experience as a human being.
Knowing all of this, it is not hard at all to imagine that at various point in our evolutionary history, many of our ancestral cousins had DNA that made proteins that just weren’t as evolutionarily useful as the proteins our cells make today.