There could well be a argument for "We booked this using your platform, you have a duty to ensure that the properties you offer have the appropriate level of insurance. In the absence of that insurance, you're jointly liable for the shortfall."

It's more likely that they're just naming every possible party in their claim so that one of them is more likely to settle. As they point out themselves, Airbnb are a lucrative target who might well have decided that making the whole thing go away is cheaper than the potential reputation cost if they don't.