I've heard people argue that the real original meaning for this commandment was murder, which doesn't include state sanctioned killing. Is this correct?

It's not correct.

Ok, that's a good thing, considering that would have some pretty god awful implications, no pun intended.

Some theists argue that some types of killing do not qualify as murder. Even as an atheist, I agree with this. There are different "degrees" of murder. Our society has decided premeditated revenge killings are "worse" than killing a guy in self defense. Our legal system takes this into account. Apparently christian law also takes it into account.