A host should carry insurance coverage of their own on the property for matters not covered by Aircover for Hosts. Go to the Host Resource Center in the app and read Everything you need to know about AirCover for Hosts. First you need to notify the guest of the damage and request that they pay to repair or replace (take photos), documenting the cost with an invoice, written estimate or link to the item price on line. If you aren't able to settle with the guest directly, you can involve Airbnb.
I had a situation where a guest stole numerous items from my house. Of course I was not able to resolve it with the guest so I had to involve Airbnb. They paid for most things through Aircover but not all. They called the theft of a laundry basket "loss of inventory" and not covered. They disallowed a claim for heavy cigarette smoke odor throughout the house (no smoking allowed). So be prepared for things like that if you need to make a claim through Aircover.