I've no idea, really; I have little experience trying to explain fallacies to anyone as part of addressing their points. If by "stating it like that" you mean the second paragraph, it was an attempt to cover more bases in case simply naming the fallacy didn't work.

I guess it depends on the audience - if we're explaining this to the archetypal Man Taken Off The Street, the simplest thing would be to just point out the differences in what law (in this case) is used to mean and forget any and all mentions of theory, fallacies and categorical syllogisms. I proposed giving a name to the error and adding detail because of this part of the OP:

The annoying part is that it is deductively valid if the definition of law is actually the same in both premises. The person making this argument thinks their argument is watertight because of its structure, and will likely not listen to any suggestion that natural laws are not a component of the laws described in the first premise.

My idea was that if someone thinks to cite structural soundness as support for their argument, it might imply they're sufficiently well-versed in the field that name-dropping the fallacy actually has a chance of working.