Dual employment can be said that, in case an employee is working with another organization while also being on the payroll of another company, not as a consultant for either company.
As you mentioned, he has left the organization and joined another one. So, logically, it can't be considered dual employment. In this case, you may try to seek compensation for the lack of notice or shortfall in notice as per the signed agreement from him. However, on the other side of this situation, if he has not been officially relieved (in writing) from the company, then he still maintains a relationship with the company as an employee and employer. For legal matters, it is advisable to confirm with an advocate or legal adviser.