The problem is that the Administration will go forward as if the EO was 100% legally binding. Whether or not it actually is legal, the only way to get them to back off would be with some entity with standing to sue over it. And even then, we have seen that they ignore orders they don't like, right up until they get to their Supreme Court, who will always carry this administration's water (and in a way that will not empower future Democratic administrations to do the same, if we ever have those again).
So while the EO, by itself, doesn't have any legal standing, in practice it will have the full force of the Administrative State behind it, and may as well be legal. That's not how things are supposed to work here. But then again, we're also not supposed to let insurrectionists take office, or play stupid parliamentary games to steal Supreme Court seats.
The media does nobody any favors by saying "Um Ackshually...." when in practice what this dictator says gets implemented immediately, regardless of what the law says.