No, this hypothetical drive isn’t just relativity incarnate. It uses a hypothetical source of negative mass. This means it has a gravitational effect the same way the moon does, but the tides aren’t just a relativistic stretching.

This ship would literally push objects away from it. That mechanic is crucial to the concept of the ship. If we were in space, in a box, with that ship near us, we would perceive the ship’s direction to be up, because the repelling effect would be identical to the equivalent positive mass below us pulling us down.

And if one of these hypothetical ships could do this to an extent that allowed it to fold space to cheat out faster-than-light movement, I imagine the gravitational effect would crush us entirely.