there isn't a definition of an EASA aircraft in the document
There isn't one in the amendment because it's already defined in the ANO.
'EASA aircraft' means an aircraft which is required by the Basic EASA Regulation and any implementing rules adopted by the Commission in accordance with that Regulation to hold an EASA certificate of airworthiness, an EASA restricted certificate of airworthiness or an EASA permit to fly;
As far as I can see, that definition includes
"aircraft registered in a Member State, unless their regulatory safety oversight has been delegated to a third country and they are not used by a Community operator" (i.e. within the BR by virtue of 4(1)(b))
and excludes
"aircraft registered in a third country and used by an operator for which any Member State ensures oversight of operations or used into, within or out of the Community by an operator established or residing in the Community;" (i.e. within the BR by virtue of 4(1)(c))
It looks like the draft amendment makes an attempt to deal with that in Art 61(1), but cites the wrong paragraph, 4(1)(d)
"aircraft registered in a third country, or registered in a Member State which has delegated their regulatory safety oversight to a third country, and used by a third-country operator into, within or out of the Community"
Personnel involved in the operations of aircraft falling under 4(1)(d) are not required by the BR to comply with the Essential Requirements for Pilot Licensing and do not fall within the scope of Part-FCL.
The whole structure of the FRA provisions is pretty clumsy (I'm not slinging mud -- it's complicated) and needs some review.