The summary is a horrible summation of the article, which itself is a lackluster summation of the actual issue.
What is actually being litigated is the fact that definitions in enabling legislation, such as the NFA, have meaning. Words like “machine gun” have statutory definitions that the President does not have the authority to selectively reinterpret via executive order, omission, or any other channel or method. If Congress would like the definition of “machine gun” to include semi-auto rifles equipped with these particular pieces of plastic, they can amend the NFA.
Same goes for the brace rule and the frame and receiver rule. The ATF does not have legislative authority and the Courts have a duty to check their power in this area.