I see some issues with your deconstruction.
ICANN had no legal obligations under international law (which by definition does not apply inside the US).
This is somewhat oddly stated. It might be better stated that "ICANN (consistent with its status as a non-governmental entity) had no specific legal obligations under international law, beyond those embodied in US law as a consequence of the US's treaty and convention obligations and subsequent lawmaking." As for the parenthetical, is your point that international law does not apply inside the borders of any country, or that the US is somehow uniquely immune to international law? I don't think the latter is correct, and the former is much more general than your statement, so I don't see the point.
ICANN has only obligations under California law, or the law of any country it does business in or with.
Well, no. ICANN also has obligations under US law (i.e., federal law), which is quite a significant matter. (Remember, we have a Congress that (theoretically) passes laws, and a President who signs them. Those are federal laws.) There may also be obligations under other state laws and the laws of the District of Columbia. Kudos for writing "California law" rather than "Californian law," which is just nails on a blackboard to me.
But, I think we are agreed that some obligations that originate from international law have been legally imported into ICANN by the choice of the founders, as per the words in Art. 4; however they remain fairly wooly.
This seems fairly straightforward, until the last bit. Not sure what is meant by "wooly". Perhaps a reference to Cardinal Wolsey. I might go with "high-level." But then again, Articles of Incorporation generally are.
I'd reprhase the question more precisely to say
"Does NTIA's disengagement introduce risk that, without the future oversight of the NTIA, ICANN would be more able to act (or fail to act) in a way that is incompatible with general principles of international law."
Based on the reference (Apple) you so helpfully supplied, "general principles of international law" is a concept that is actually completely different from the concept of international law as "laws between nations" or "laws established or on the basis of a treaty or convention." Instead this refers to principles of internal laws of countries that are so widespread and common that they can be seen as "general principles" of the law of [nearly] every country. The author cites the law of contracts or murder as examples of areas where you will find general principles that are common to the judicial systems of most countries. Broadly stated, Apple (quoting Janis) states it thus: "The basic notion is that a general principle of international law is some proposition of law so fundamental that it will be found in virtually every legal system." As such, the general principles of international law will be found in the legal system of the United States (federal law and applicable state and local laws and regulations), just as they will be found in virtually every other internal legal systems. Thus, virtually all "general principles of international law" will be found in the laws applicable to ICANN. Therefore, ICANN as a entity subject to those laws is prohibited from acting (or failing to act) in a way that is incompatible with general principles of international law, because those actions (or inactions) would violate US federal and California law. It is really the fundamental precept that ICANN (like every other person and entity in the US) is prohibited from breaking the federal and state law that prevents ICANN from acting incompatibly with general principles of international law -- not the NTIA contract. Sure, NTIA like any public or private contracting party has various rights to get out of contracts with parties who are breaking the law, but this is not unique to the NTIA relationship or to the fact that the NTIA is a government agency. The NTIA relinquishing its agreement does not in any way provide carte blanche to ICANN to go around breaking the law. So, my conclusion is that the NTIA disengagement does not introduce any substantial risk that ICANN will be more able to act (or fail to act) in a way that is incompatible with general principles of international law, because ICANN will still be under fundamental obligations to comply with US federal and state laws, which by definition embody "general principles of international law" per Apple and Janis.
Greg