Why is a modern president considered the country's chief legislator and chief policy maker?

He is the country's chief policy maker because as chief executive - in whom the entire executive power is constitutionally vested - he is in charge of the executive branch, which means he can direct each federal department or agency to establish his policy priorities. There are several tools of agency policy making, like regulation or affirmative adjudication, for which the President can set guidelines, consistent with his own policy wishes. Of course, if a policy the President wants to be established, violates the law, Congress has to change the law.