The Arishok thinks he's not going to get the book. His mission was to get the book. Is it possible his attacking Kirkwall has an element of 'glorious suicide' in it? Death in battle might be prefereable to him under the Qun than sitting there doing nothing for the rest of his life.
That's a very interesting thought, and quite plausible. He's extremely cranky about being stuck there looking for a book he can't find, and after Isabela runs off with it he has reason to believe he'll never see it again. He seems to have a few hundred troops at most - maybe enough to burn Kirkwall, but I doubt it would have been enough to hold it once reinforcements arrived from elsewhere. Even if the Champion had fallen in battle against him, there's no reason to think Orsino wouldn't have stepped into the room and set all the Quanari on fire ten minutes later.
(I would love to know how he does that in the cut scene, since in my game they're immune to fire damage! Maybe Orsino plays on Casual.)
Either he meant to raze the city and leave to go after Isabela, or he was expecting to die. While you're duelling him, he says a lot of stuff about how even if you defeat him the Qun will be victorious in the long run. His own death probably doesn't matter to him much.