Such a definition of systems language strikes me as borderline useless and vague, though, hence my request to chuck it out the window. (See also: high-level vs low-level is an even more poorly defined and useless term). I also don't see C (or rust, or C++) as having any unique affinity for accessing hardware—certainly, certainly not better access than lisp, which can often resemble an assembler with twenty megabytes of macros baked on top. Hell, I'd argue lisp is more systems-y and "low-level" than C is, which can't even be easily utilized to pump out a maintanable boot sector. It's just not built for that; it's built to generate object files, which then need to be lowered into binaries with a linker. Lisp is just flexible enough to rewrite itself into the target domain, which C cannot do.

Look, I'm not trying to argue about definitions; it's a waste of both our time. But genuinely, why are you so strident about using the term if you clearly have a more precise understanding of what you want to communicate? Why not just say "programming languages with access to an inline assembler and address lookups" (which, again, would include most common lisps)? Why not say "can link to the C ABI without relying on FFI at runtime" (which would exclude many lisps)? And granted, this only came up because it was used seriously in the original post, so the onus is really on everyone to care about how precisely they characterize language.

We should honestly just stop using "systems/high-level/low-level" entirely; they're too vague and get people too worked up. Which is just baffling to me; I have no emotional attachment to any programming language or similar tool.

Edit: you may find Game Oriented Assembly Lisp interesting: https://en.m.wikipedia.org/wiki/Game_Oriented_Assembly_Lisp