According to the article, the Supreme Court test is this:
- "When the President acts pursuant to an express or implied authorization of Congress, his authority is at its maximum, for it includes all that he possesses in his own right plus all that Congress can delegate. In these circumstances, and in these only, may he be said (for what it may be worth) to personify the federal sovereignty. . .
- When the President acts in absence of either a congressional grant or denial of authority, he can only rely upon his own independent powers, but there is a zone of twilight in which he and Congress may have concurrent authority, or in which its distribution is uncertain. Therefore, congressional inertia, indifference or quiescence may sometimes, at least as a practical matter, enable, if not invite, measures on independent presidential responsibility. . .
- "When the President takes measures incompatible with the expressed or implied will of Congress, his power is at its lowest ebb, for then he can rely only upon his own constitutional powers minus any constitutional powers of Congress over the entire matter. . ."
The way that reads to me is that if Congress makes a law that gives the president the authority to do something, then he has the ability to issue Executive Orders to enact those responsibilities. That's pretty clear, and logical.
Conversely, if Congress makes a law specifically denying the president some authority -- or if the president does not like the law -- he really has very little ability to issue Executive Orders that run contrary to the law. Also clear, also logical.
Where the gun issue would seem to fall is point #2, the "zone of twilight." Obama could argue that Congress has, through inaction, enabled him to take specific action on guns. Congress can then try to pass a law challenging the president's EO (which I doubt would succeed, given the Democratic control of the Senate). And it could also be challenged in court.
Maybe you're reading it differently but that's how I see it.
EDIT: Roosevelt's attempt to pack the court was a totally different deal. That was a bill in Congress that would have given him the authority to name additional justices which ultimately failed because it wasn't popular (and a few other things). It wasn't an EO.