The argument falls apart at every single step. As a logical deduction it is awful. The premise is just straight up false. And the rest also has obvious holes.

Simple counter example:

If every single person in a population can employed for economic gain by an employer, even if the employer was paying minimum wage, then having a minimum wage would not change anything about employment. An employer would obviously rather make some gain of an employee than not making that gain at all, so no changes to unemployment would happen.

There are obviously ways in which employers can increase the profit they make from employees. E.g. by raising the cost of their products.