I would certainly say that it was part of the same family of movements as the 6664 but there are a number of differences.
The 6664 has a push pin stem release and an adjustable stud carrier. The OP's watch has a screw stem release, a fixed stud carrier, and a completely different set lever bridge/spring. It also has a cut away around the outer edge of the train wheel bridge, although this may simply be cosmetic.
I'm not saying that it definitely isn't a 6664 as it is not uncommon for there to be slight variations within a particular calibre, however, this level of deviation is usually accompanied by a change in designation.
Of course it may make no difference at all in this case as it could well be that the same balance staff is used across the whole movement family, but then again if there are variations in (for instance) beat rate within the movement family, this may also mean variations in balance design and potentially different staffs.
It goes without saying that whatever it turns out to be it needs a non-shock protected staff and not the Incabloc illustrated on Ranfft.