Well, here's some attempt at an answer.

From the prophecy (ch.1) we know Alfonso the Good is the 'real owner' of the castle of Otranto.
Alfonso lay within it's walls, unable or unwilling to ascend to heavenly rest until his true heir was restored.

Perhaps the castle was a great tomb for Alfonso, body and soul.
Just after Theodore revealed himself as prince-
Alfonso is ready to ascend bodily into heaven , literally !
His ghost 'grown too large to inhabit it' breaks free of his earthly castle and crashes the walls down.

Alfonso's spirit no longer requires earthly confinement or defence which is what the walls symbolize.

It may have been important to the author to note the walls falling.

Sovereign princes usually had more than one castle of residence.

Of course, it may've just been the earthquake which brought down the walls, but who wants to believe in reality ! ;)