"And even other than that, machine code isn't dynamically typed because it's not typed at all."

Well, we have bytes, words, doublewords and quadwords on the machine level. They are usually referred to as data types in the processor manuals.

I'd say that instructions are typed, but data are not. You can use an integer arithmetic, bit manipulation, floating point arithmetic, or vector SSE instruction on the very same data in the very same register, and it will just work without any complaints for most bit patterns. A CPU of course does analyze the code, but only the short segment currently in the pipeline, and not for any high-level semantics, just for data dependencies and very local jumps.