I don't think you will be able to reproduce this without the Asus - 14" ZenBook Duo Touch Laptop. So this is just an FYI.
If the form that contains the TAdvDirectoryEdit opens the browse dialog from that control where it spans both screens and the [OK] and [Cancel] buttons are cut off (below the lower screen), they will not be there even if you drag the browse dialog to the main screen. If it was originally opened on the main screen, it is fine.
I tried to duplicate it on my monitor where I had the dialog open such that the OK/Cancel buttons are below the bottom of the monitor out of view, I can drag it up and all is still there. So it might be something specific to that notebook dual screen configuration.
I did however notice that if my main monitor is set with windows scaling at 100% and the secondary monitor is at 125%, the buttons do disappear if I drag the browse dialog fully into the secondary monitor, but come back when brought back into the primary monitor. So it might be related.