You are incorrect in that you are describing what is an Executive Order (EO)Obama did not have to use an EO or legislation as there was already an existing law. All that was done was Obama used the 1953 Outer Continental Shelf Lands Act to withdraw leases and ensure that leases do not exist in the named areas of the Act.

43 U.S. Code Subchapter III - OUTER CONTINENTAL SHELF LANDS
https://www.law.cornell.edu/uscode/text/43/chapter-29/subchapter-III