On that turn 14 there seem to be multiple 'options' to freeze the game. As described by kingdedede, when his opponent has the option to trash a card for the Bishop kingdedede played, all possible actions end in a freeze. If he selects a card to trash, the game will freeze with the red "X" 'selected for trash' marker on the card.
I tried other ways to play that turn 14, to see what happened. If you (as kingdedede) play turn 14 (decision 108) Crown+Bishop, and you choose to trash the Estate twice (it comes back because of it having the text of Fortress), the game freezes on your turn right then. If you choose to trash other cards (not trashing the Estate, or only trashing the Estate once), then you can end your turn. However, the AI opponent always started his turn by playing Bishop itself and trashing an Estate (that is also a Fortress due to Inheritance) and the game will freeze then.
My suspicion is that after the Estate comes back to the hand the first time after being trashed, something is slightly incorrect about it. When it is trashed a second time, something goes wrong.