The Casino of Chatby is smaller that a Basilica; but it is not necessarily on that stone platform [on which the Casino stands] that the Basilica stood. My impression is that on the site of the Martyrium --originally a small chapel built on the tomb-- a larger church was then erected, but not only a church...there were certainly many other buildings. We have to think of something that attracted pilgrims so there was the necessity of more than a church.
The fact that in 1218 the governor of Alexandria decided to put down the church, because he feared that it could be used by an enemy army as a stronghold for an attack, speaks for itself. A church, even a large church, would not present a threat but there probably was a complex of buildings.