I think of the runtime as the whole execution stack. The interpreter, engine, JIT etc. is the back end. The interface to the world is a wrapper around that.

I would describe this as a Lua wrapper written in Rust. That carries the clear indication that you should not expect the interpreter to be written in Rust.

I would be (and indeed was) disappointed to see that this 'Lua runtime' did not have a Rust implementation of Lua. I would be much more interested in seeing that than a wrapper.