You're right, it's much more about context than vagueness. It sounds like Grayling was celebrating the power of context in enabling us to convey a great deal of information with few words (though in this case the tone and manner of delivery would also be a key factor). On the other hand, there is a link to vagueness in a broad sense of that word--probably too broad for most philosophers these days 'Fire' on its own can mean many things. In that sense it is' vague'. Context and other factors help to disambiguate it. In fact, 'vague' is here being used as more-or-less synonymous with 'ambiguous'. In recent philosophical logic, however, 'vagueness' means something much more specific. It is exemplified by a word like 'red'. Some objects are clearly red. Others are clearly not red. A third category consists of objects that are borderline--a kind of orangy redness that is hard to classify one way or the other. Furthermore, there is no precise boundary between the things that are clearly red and the things that are borderline, or between the things that are borderline and the things that are clearly not red. Many terms exemplify this sort of pattern--in fact our language is full of them. (To take another example consider: exactly how many hairs does a person have to have to be able to escape being 'bald'? There appears to be no precise answer.)

If I got it right, Grayling's example is issued to stand for a "sample" of vagueness and you claim it's basically a matter of context. 
Now, even if the example proved wrong (since "Fire!" could easily convey both the intention and the reference of his message, hence its precision), it doesn't mean that "context" would become all that matters when dealing with vagueness, if anything. Ok, perhaps Grayling's instance is not illustrative. But it doesn't mean that in any circumstance the power of context is a touchstone. If I were to teach an Indian my language, would s/he claim some words are vague? If yes, would it be a matter of context? It depends on the meaninf of "context", which brings us back to vagueness.

I think Grayling was using the word "vagueness" a bit loosely (if not downright incorrectly), at least as far as philosophical terminology is concerned. Not vagueness, but ambiguity is the property exhibited by this utterance of "fire!" - it could mean many things, but, as you say, context makes clear what it does mean.
The utterance would exhibit vagueness, on the other hand, if the [implied] claim that "there is a fire" lacked precisely specifiable truth conditions, resulting in the possibility of borderline cases -- of 'almost-fires' or 'maybe-fires'! -- in which it failed to take a determinate binary truth value.

So the distinction, on my understanding (I'm just finishing an undergrad. philosophy of logic course, but am relying on memory and haven't bothered to consult my sources for this post) is as follows: ambiguity = meaning dependent on context, while vagueness = no precisely specifiable truth conditions.

Incidentally, I don't know if Grayling actually used the phrase "any logical person", but, if so, extra demerits for that; I am aware that words have quite distinct colloquial and technical senses, but, still, the employment of the term for the study of deductive entailment to denote a caricatured cold-blooded Vulcan-style rationality really annoys me! :-p