This is an intelligent propaganda move, and I would expect to see more of it from AQAP, although it does avoid saying exactly what it would do, but in a statement like this that doesn't matter too much.
The statement basically runs along the following lines:
2. Condolences to those injured and suffering from the flooding
3. Sharp attack on the Saudi government for being corrupt, stealing money and lining their own pockets while the citizens whose care they are entrusted with suffer.
4. Call to arms (for those interested in that particular style of onomatopoeia in Arabic check out lamlama in the 10th paragraph).
I don't think we should underestimate how powerful things like this can be over time in eroding a government's moral legitimacy.