What's the difference between mechanical and hydraulic brake rotors?

There is no distinction between mechanical and hydraulic in terms of rotor compatibility per se. The manufacturer may be trying to get at something else in a clumsy and arbitrary way. They could be saying it's a direct replacement for the rotor that comes in some other brake set they produce, or they could be falsely equating mechanical brakes with using only organic pads, or it could be a dainty ultralight rotor and this is their way of cautioning against subjecting it to the generally higher (debatable) temperatures that might be encountered in a hydraulic system being used in a more demanding brake application.

The compatibility distinction you want to make sure you're not on the wrong side of is using metallic/semi-metallic pads on a rotor for organic aka resin only. But it's not clear that's what you have if that's the only verbiage they give you to work with.