Per definititon, well depths are always referenced to a datum,...

Per definititon, well depths are always referenced to a datum, which in this case is MSL (Mean Sea Level). Drillers sometimes reference the rig floor or the Kelly bushing (before they used topdrives), which is a bit higher. But for consistency, every offshore well is referenced to the same datum that the oil companies use, which means that it does not depend on the height of the rig floor above the water.

Onshore is similar, but there the reference is normally ground level, but that is referenced to MSL.

That means the water depth will be included in the drilling depth.