I don't fully understand who this style vice is actually for, and despite looking very cool, there's a reason nobody has these things 100+ years after their invention.

A woodworking vice typically has softjaws and despite the flexible-ish nature of this vice they still would leave marks in wood so not much help in the woodshop.

A metalworking shop typically uses vices to hold work that they are going to beat on with a hammer, lean on it with a pry bar, attack with a torch, and generally use as a super-secure hold while applying a lot of forces to the work. The vice here has a lot of precision moving parts which wouldn't really hold up to that sort of use case.

A machinist vice is a precision tool and the fixed jaw is a reference surface for the work. With suitable stops, one can use a machinist vice to place work into a predictable position time after time ("repeatability"). This style of vice can't do that either.

I could almost maybe see this used for small parts fabrication on a drill press maybe? The OP uses it as workholding while engraving which feels a little contrived and there are other cheaper/faster/easier solutions out there but sure maybe?