This would not affect, for example, the people who engineered the Sony data breach or any of the various cyberattacks against retail or service companies that have been in the news in recent years.
Your worries about the constitutional basis for executive orders are misplaced, I think. Bear in mind that the President is in charge of the executive branch; this order promulgates a policy rule for executive agencies, ie, should the relevant event occur, DoJ is instructed to launch proceedings* to have the assets frozen. Think of it as a statement about how the administration will exercise its lawfully delegated powers going forward.
Edit: I said DoJ but the process starts with Treasury adding the person to the SDN list and proceeding from there by established means, though the doJ would get involved with that down the line, most likely. Sorry if that was confusing.
* by applying to a court for the authority, not on its own authority or on the authority of the order itself