I might have missed it, but key is that DNA is not executed linearly. Instead all instructions are executed all the time. Much like the difference in normal programming and programming an FPGA, but then probabilistic.
That statement is only true in a very narrow context.
Much of your DNA is silenced by being formed into dense chromatin - DNA that is tightly packed onto a protein scaffold. However, the regions that are silenced change throughout development, and these regions are not strictly inaccessible. This is seen with CNSes, conserved non-coding sequences. As the name implies, these are not traditional genes that make protein products, but are usually small regulatory sequences that often affect chromatin state, and sometimes at a great distance. I've had colleagues attempt for years to identify a mutation, only to find it that the causative change occurred many kilobases away from the relevant gene. This is partly the reason why DNA is not 'plug and play', as the genomic context of a particular sequence often matters.
Which is why DNA isn't really linear, at least on a genomic scale. The processes of transcription and translation (DNA -> RNA -> Protein) are linear to be sure, but the regulatory networks that determine gene expression are happening all at once on a massively parallel scale. These molecules are also 3-dimensional and can fold back on themselves and cause modifications. Essentially every fundamental process in gene expression is able to be regulated, whether it's enhancers and repressors affecting transcription, RNA-mediated silencing, RNA splicing, RNA modifications and stability, histone modifications, protein modifications, protein stability, phosphylation or any of the dozens of other post-translational regulation, and on and on and on.. And there are thousands of genes which can impact all manner of other genes at any of those levels, either directly or otherwise. It's a wonder that we're able to tease anything out of it that makes sense.
Generally speaking, I caution against computer analogies for biology. Biology is messy! It rarely works how you want it to. Even relatively common and basic techniques in molecular biology require a great deal of troubleshooting, and even in the best labs with loads of experience, sometimes things simply refuse to work how you'd like them to. You don't hear too much about synthetic biology anymore (it's still going, just less hype) because the premise was incredibly naive; you were never going to get bits and pieces of DNA to behave in a predictable manner. Just about everyone with wet lab experience suspected this.
For context, the current hype about CRISPR is almost entirely based on how well it works, not what it does. We've had a few different techniques for modifying DNA for a while now, but none of them worked quite well enough to practically accomplish all the interesting things that CRISPR is now enabling.
