It sounds like you may have already read the
recent FAQ about hydraulics.
If I understand your setup, you are releasing water from one cup into another and presumably using the weight of that water to initiate some action.
To the extent of my understanding, they would define two syringes hooked together as "entirely enclosed" since there is no water exposed to atmospheric pressure. I don't think that pouring water from one cup to another is at all "enclosed".
Looking at, for example, hydraulic brakes:
There is a reservoir that the system draws from that is essentially open to the air. It is usually covered by a plastic cap to prevent spillage, but it isn't sealed against pressure or anything.
The fluid is drawn through the master cylinder setup and taken to high enough pressures to provide the force on your car's brakes.
To me, like the windshield-fluid pump setup that I advocate, it is a clear demonstration of hydraulics. The part of the system where force is actually being transferred (where the hydraulics is happening) is enclosed and pressurized, but there is the "open" reservoir that the system draws from. I dunno.
Either way, I don't think pouring water between two cups is enclosed.