Edit: To clarify, by "this sort of thing" I don't mean "Airbnb like businesses". There's nothing particularly novel about insuring homes, their contents or vacation rentals. An institutional insurer can crunch some numbers (with estimates on the average values of contents, caps on liability, frequency of incidents, cost of claims inspection, rate of fraud) and figure out what the risk profile on that is and then mark that up and sell it to Airbnb.
What's actually unclear to me, however, after crunching out a revenue estimate for Airbnb (which I'd assumed was higher) is if they're a big enough fish yet for an insurer to bother with them.