The EASA angle is one of the very limited occasions where a non-ICAO entity has compelled a group of ICAO signatory states to force flight crew licensing regulations onto foreign states' aircraft.
It is not clear what you mean by a non ICAO entity. EASA is no different from the CAA in respect of it relationship with ICAO. It has been established by 27 contracting states acting together to full certain functions on their behalf, including the development of legislation giving effect to ICAO standards. The legislation establishing EASA is a Regualtion of the Council (representating the governments of the EU Member States) and the European Parliament (representing the voters of the EU Member States) adopted in accordance with a procedure set out in a Treay to which all the EU Member States are party.
Under the Regualtion EASA's key role is to develop implementing rules to support the essential requirement of the Regualtion. However, EASA does not have the power adopt the rules itself. Rather they are adopted under the EU legisaltive process. The Member States representatives vote on the proposed implementing rules in relevant committee. The rules are then subject to scrutiny by both the Council and the Parliament who may reject them if they are not compatible the intent of the EASA Regulation.
EASA was given a clear mandate in the EASA Regualtion in respect of the licensing requirements for third country aircraft operated by EU residents. Therefore this is a clear case of the contracting states telling EASA what to do. It is not a case of forcing flight crew licensing regulations onto foreign states' aircraft, rather it is the EU governments establishing a licensing system for the EU and ensuring that EU residents comply with that licensing system.