I am an attorney, but not familiar with South Dakota law. On the surface, that requirement does not appear legal and binding. I bet it is something that was drawn up from within the company, probably by a manager thinking they would be doing polygraphs. I can tell you that doing random polygraphs would be cost prohibitive and would yield nothing. Those tests are not rock solid, and testing all employees with the question, "Have you ever stolen anything from the company?" would yield a positive from someone who considers taking home a paper clip stealing. Half the employees could respond positive to that question.
I would not worry about that clause. If it is a job you want, then sign the agreement. It probably is not legal and enforceable. The likelihood of random polygraph tests affecting your employment is slim to none.