Seriously, US forces assisted in the toppling of the previous imposed Afghan government and in the establishment of a new, democratically elected government. That was a strategic effort which was completed. That was followed by an operational effort to assist the newly formed government using FID authority under a Congressional Resolution and with continued support by Congress at that level. That supported Afghan government is in no position to launch a strategic initiative at this time so they are unlikely to attack Pakistan. Nor are we likely to do so as it isn't in our interest.

Thus it seems to me that the answer to your question is that no one has taken the strategic initiative; the 'D' in FID is Defense and that is what's occurring. You should be concerned with the legal aspects because that is the intent of the paragraph you quote.

On a practical rather than a legal level, people are making things go 'boom' and people are being killed -- that makes it a war, as I said earlier, a war with COIN like efforts included:
war (wôr)
n.
1.
a. A state of open, armed, often prolonged conflict carried on between nations, states, or parties...
A for real war in dictionary and practical terms if not one in US legal terms.

You and others may call it a COIN operation if you wish, you may call it FID if you wish. You may call it frangipani if you wish. You may also play with 50 USC 33 if you wish, I'm not going to do that and I'll call it a war because of the killing and dying. Besides, Joe will want to tell his Grandchildren he was in a war...