The vises with the "deep V" are called offset rotary vises.
Vises which are rotary, but not "offset rotary" are called "in-line" rotary.
Nor vise has its original jaw system which was/is in-line rotary. It is, however, probably first, and foremost, for spinning.
Regal Engineering now carries a well-made in-line rotary vise called the "Revolution"
Out of curiosity, why do you not want an offset rotary?