My idea was that the US is fulfilling the ally obligations towards these governments. ISIS itself is not a recognized sovereign, so it cannot be declared a war to, thus no congressional approval.
The rise of non-state actors has definitely complicated public policy regarding the use of force. IANAL, but it seems like much of the legal frameworks around use of force, just war, etc. is predicated on Westphalian sovereignty, which doesn't really have a place for groups like ISIS, Al-Qaeda, Hezbollah, Iraqi militias, etc.