Except that it doesn’t represent logic, it represents strings of amino acids that form proteins that fold up in unpredictable ways and interact with lots of other things to do stuff that half the time is weird and inefficient and doesn’t make sense.
There's quite a bit of logic encoded. DNA has equivalents of conditional jumps, and stored state. That's in the stuff that for a long time was called "junk DNA" between the encoding sequences.
I wouldn’t compare it to machine code alone and for it to be considered following under rules that can be broken down fundamentally to appeasing what we define as logic. I think of recursive functions calling other recursive functions with returning variables that effect the whole mess of a system when I read the perverse alterations to the animals in the article.