Web UI moves are rate-limited in MovePageForm::doSubmit(), which ApiMove has never used.
I note that MovePage (the utility class for moving pages) is a bit too low-level for the purpose, since it handles moving exactly one page while the rate limit should probably continue to apply to "submissions" that might move a page, its talk page, and its subpages all at once.
Filing this as "security" since it allows for bypassing rate limits.