@drkirkby: You are correct with respect to the source or load impedance, it should be specified.
Especially wide band EMC antennas have varying VSWR across the band and you can't make a matching network that covers the whole band. It is therefore convenient to specify gain based on incident power (or maximum available generator power).
This document:
www.conformity.com/PDFs/0712/0712_F05.pdf deals with EMC antennas. On page 43 (under Directivity and Gain), it mentions why they deviate from the Gain definition as used in IEEE.