No. "Retrying with admin rights" would require launching a new process
with admin rights and then retrying. AutoHotkey can't detect the dialog, and doesn't even know which files are being copied. When the source and destination are on the same volume, the move is handled by a single call to
SHFileOperation(&FileOp).
If you run the script as admin, the first try will be "with admin rights".
If it's even possible that FileMoveDir is causing that dialog, I suppose that it is a bug in Windows (or its documentation).
FOF_NO_UI
Windows Vista. Perform the operation silently, presenting no UI to the user. This is equivalent to FOF_SILENT | FOF_NOCONFIRMATION | FOF_NOERRORUI | FOF_NOCONFIRMMKDIR.
Source: SHFILEOPSTRUCT structure (Windows)
AutoHotkey doesn't use the FOF_NO_UI constant, but it uses flags which combine to exactly the same value.