Well, yes, but that's the easy bit: clearly it means that there hasn't been a worse storm in the interval between 1984 and now. The hard bit is, what do we infer about what happened in 1984, if we don't already know?

We probably presume that there was some sort of really bad storm in 1984; if there wasn't, you probably wouldn't have said 1984, you'd have said "worst storm since 1927" or some other earlier date. But was the storm in 1984 worse than this one? Perhaps it was (on the same grounds). Or perhaps it wasn't as bad ("this storm was so bad it pushed 1984 off the top spot"). Or perhaps you yourself aren't sure whether the 1984 storm was worse or not, and are making the strongest statement you're reasonably confident of.

Or, conceivably, you might have said 1984 not because it was the date of a storm at all but merely because that's as far back as your records go.

1984 would have to be a worse storm than the recent one, because otherwise the recent storm would be the worst one since a longer ago storm that was worse than the 1984 one. This is the law of weathermen: always compare things to the most historical thing you can.

Wouldn't you then say "worst storm since record began?" Saying 1984 would be too ambiguous - people would probably think that there was a worse storm in 1984, but they wouldn't think that there was a worse storm "when records began"

Well, this is precisely the question under consideration! From the poll results so far, it seems to me as if only about 40% of people would naturally assume there was a worse storm in 1984.

Certainly saying "since records began" or better still "since records began in 1984" would be clearer; the question is, would it be so much clearer that you're entitled to infer that that's not what I meant or else I'd have said it?