Third party bookings are not allowed although apparently AirBnB is working on a policy to allow this.
For you it probably now depends on the circumstances: did they lie to you during the booking process, if so I would be concerned and contact AirBnB and ask them to find alternative accommodation. In a challenging situation you are not covered by the Host Scheme for these bookings.
Was it just never mentioned and it is someone booking for their parents, or similar....? While not allowed either, it's certainly a different situation to where you feel you have been misled.
In future you should always confirm that the person booking is staying too.
Remember AirBnB checks are not background checks - they just verify that the person who is using the account is who they say they are.