I was somewhat avoiding bringing that up just because, in theory, every physical 'system' in the universe just boils down to physics—and this question gets pretty close to the line between where it's useful to start talking about a higher-level system, versus thinking in terms of chemistry (and/or physics). So it could get confusing.

If there is a higher level system analogous to a runtime-environment which could be abstracted from actual genetic machinery, I would bet the rules of its operation would still be at least partially in terms of chemical rules (in other words, you couldn't abstract over it entirely).

My justification for it is that I think the system is split between the decentralized behavior of proteins and enzymes etc. just following the rules they always follow, combined with the external 'system' which sets up conditions constraining and otherwise directing the proteins. That second system could maybe be higher level, but it's still central to its operation that it interfaces with a 'raw' chemical system. (Just an idea of course—my confidence that it means anything is ~12%).

Edit: another analogy to maybe clarify (or confuse) things. I see the proteins/enzymes etc. which I described as decentralized as operating like a cellular automaton (e.g. Conway's GoL), but then the 'external'/centralized system as like another layer of rules which sort of pushes around clusters of cells in the grid in various significant ways, while all those clusters are still locally just executing the simple automaton rules.