Here is MikeF's question:

If the drug cartels are adding oil as another business set, at what point do they become an insurgency? Is it possible that they are currently setting up shadow governments and controlling portions of territory?
and Wilf's answer:

They become an insurgency when they try to replace the existing government as that which exercises authority over them, and use violent means to secure that policy.
which is correct as a military definition. However, it is not the final answer as to what law and rules apply in engaging them.

Drug cartels and criminal gangs in general are Violent Non-State Actors. In their present-day highly evolved form, they are usually Transnational Violent Non-State Actors. Calling them that does not necessarily tell us what to do with them - it only defines what they are.

Nor, does it necessarily help to define them solely in terms of an insurgency. A transnational gang may not be violent on its home turf (it may already own that government, for example). It may be very violent in another country, but not have either the intent or ability to overthrow that government.

Cutting to the "cheese" (because I have an 87 year old, WWII 82nd Airborne vet, waiting to sign some docs), under US law, a state of "armed conflict" can be "declared" against a Violent Non-State Actor, as in the case of AQ.

Normally, we (US) handle gangs under criminal law enforcement rules.