Hi Ron,
WGS84 does not have a Vertical Datum. What it has is an Ellipsoid, which is a mathmatical representation of Mean Sea Level. EGM96 is a Geoid, which is a measured, lumpy, irregular surface that aims to accurately represent Gravitational Equipotential. The difference between the WGS84 Ellipsoid and EGM96 is called the Geoid Height. Ain el Abd Coordinate System (EPSG:4204) is based on the International 1924 Ellipsoid.
To answer your question of "what is the vertical datum of ain el abd?", it is whatever Geoid Model you choose to more accurately represent your surface elevations.
Dave