A typical executive order simply designates procedures and requirements to be followed by people working for the Executive branch of the government.
Which is EXACTLY what this executive order does. It is implementing at the Executive Branch the legislation to which it is based, namely the National Security Act of 1947 as amended. It even says so at the start of the order:
by virtue of the authority vested in me by the Constitution and the laws of the United States of America, including the National Security Act of 1947, as amended, (Act) and as President of the United States of America, in order to provide for the effective conduct of United States intelligence activities and the protection of constitutional rights, it is hereby ordered as follows:
Also, nothing in this executive order "led to" the warrantless wiretapping as alleged in the story. In fact, there are several places in the order that state that if US citizens are involved, it MUST go through the FBI / Attorney General. Read it. You will see what I mean.