Is employee (X) entitled to claim compensation for additional work he performs for other companies belonging to the employer, which he carries out during official working hours without remuneration, and from which the employer financially benefits?

The employee is a special hire whose benefit is measured by time. The employer owns his benefit throughout the duration of the hire. If the administrative tasks requested by the employer fall within the employee's scope of work and capability, then he has no right to refuse or demand extra pay, because his benefit is owned by the employer during this period.