Yes, during the rental period both the owner and renter are insured by Allianz. Any damages that occur during the rental period will be handled by Allianz. As an owner you will therefore not have to reach out to your own car insurer.
The insurance by Allianz includes full casco coverage: this means you are extensively covered against damage, theft, and vandalism. However, damages due to technical defects on the vehicle caused by (natural) wear and tear, are not covered.
In the event of a collision with a counterparty, all passengers are insured for the damage they suffer as a result of an accident. However, when the driver is at own fault, the driver will not be covered (but any other passengers will). When the driver is at fault, any damages can be addressed to his own health insurance.