Jack's reading of the 2002 AUMF is more than plausible. And I wouldn't be surprised if the executive branch adopted that reading, in searching out a statutory basis for military action against ISIS.
With that said, Jack's interpretation rests on a plain-language reading of the operative part of the 2002 AUMF, Section 3. And in that respect, it gives short shrift to the other statutory language---which, when accounted for, might undercut Jack's view and make the 2002 AUMF less attractive as a legal option, so far as ISIS goes.
Have a look at the operative language once more:
The President is authorized to use the Armed Forces of the United States as he determines to be necessary and appropriate in order to ... defend the national security of the United States against the continuing threat posed by Iraq[.]
What did Congress have in mind, in using the term "Iraq?" Jack answers by pointing out that there's no geographic qualifier in this critical part of the statute; moreover, words like "Saddam Hussein" or "government of Iraq" were conspicuously omitted. All this leads him quite reasonably to conclude that the President can determine, right now, whether any group in Iraq poses a threat to the United States that warrants a military response---even a group outside Iraq, to the extent it supports activities ongoing inside the country. To put the argument another way, if something or someone threatens U.S. national security, and involves Iraq, then under the 2002 AUMF, the President can use force. Obviously ISIS fits this bill.
Here's the thing though: Section 3 is not the only language in play. In fact there very much is language nearby in the statute, which informs the meaning of "Iraq," and (to my eye) points to a narrower congressional intent. Take Section 2. Congress there expressed support for the President's efforts in ensuring "that Iraq abandons its strategy of delay, evasion and noncompliance[.]" That smells like a reference to government action to me.
The statute's preamble does too, for the most part: it speaks, in one place, of "Iraq's war of aggression against and illegal occupation of Kuwait[,];" in another place, of "Iraq's repression of its civilian population" in violation of human rights norms; and in still another, of the fact that, in 2002, "Iraq had an advanced nuclear weapons development program that was much closer to producing a nuclear weapon than intelligence reporting had previously indicated[.]"
In light of these and other phrases, Section 3's reference to "Iraq" might properly be read in a narrower, more government-centric fashion---one narrower, at any rate, than the reading Jack proposes, and one not obviously applicable to a military campaign against ISIS, whether in Iraq or elsewhere. (It is true that the preamble isn't uniform in this regard: though it refers repeatedly to actions taken by "Iraq," it also contains stray references to the "Iraqi regime." But, considering the examples above, it seems to me that the preamble almost uses "Iraqi regime" and "Iraq" interchangeably.)
Don't get me wrong: I don't think a preamble or other statutory language should automatically "trump" the plain meaning of an operative statutory phrase; for that reason, I think Jack's is a plausible reading of the law. Still, the statutory context could (and in my view, probably should) matter going forward, because it points to a particular congressional objective at the time of the 2002 AUMF's enactment---which seemingly was not to authorize freestanding counterterrorism operations in Iraq and Syria, some two years after the White House declared the Iraq war's end, and five months after the Administration publicly called for the 2002 AUMF's outright repeal.
(Of course this may prove to be a moot point. The President said, earlier today, that he won't be sending "U.S. troops back into combat in Iraq;" it remains to be seen whether the United States will pursue some other military option.)