The author doesn't go far enough; eval operating on strings is still very weak (unless your language is something like BrainFuck that really doesn't have a more structured representation available). The point is exposing the structured form that the language implementation runs as datastructures within the language - and not as some second-class reflection API, but directly as they are. You want to be able to capture something like an AST representation (not necessarily literally an AST), manipulate it, and then run it.
I think "Bicameral" isn't really a great way to capture this, because there are often multiple layers of parsing/lexing/compilation/interpretation and you might want to hook in at multiple of them (e.g. in lisps you may have both reader macros that operate at a low-level stage and higher-level macros that operate after parsing). And of course it's a spectrum, but essentially the more the language exposes itself as a set of compositional libraries rather than just being a monolithic service.
