No, neither the Almaz nor the Ramada are responsible for the accident
that occurred while the employee was off duty and attending to his personal business.
If the employee had an accident while chauffeuring the guest during regular working hours, this would be different, but no employer can be held responsible for their employees once they're off work.
If the hotel had a clause in their employee contract stipulating that employees cannot date guests under any circumstances, then the employee would be in breach of contract and subject to immediate dismissal. Yet, the employee would still be responsible for the accident, regardless.