That makes more sense. Yes, it is nice that the Alcubierre drive, being within the realm of general relativity, can be described mathematically. The equations work both ways, so on one hand you can take a given distribution of matter and energy and predict how space-time behaves around it, or in this case you start with the behavior of space-time that you want and the equations tell you what sort of mass-energy would create it. Of course solving the equations in that direction easily leads to unphysical situations or impossible mass-energy requirements, but if you take those as given then the math still lets you describe it, as in if you did have an Alcubierre drive, then what would it look like?

For a "ZPE device", I think describing how it would work (in even the impossible sense) would be up to what kind of assumptions someone wants to use to model it. Zero-point energy is a real thing, but there isn't a clear physical framework to describe how you would power something with it.