Where is the “labyrinth plate” of a dishwasher

The green wire is the dishwasher's ground wire. You hook it up to the circuit's ground wire, which is the bare copper one.

The green wire ends up connected to the chassis of the washer through the connector on the gray wire. If you'd open up the dishwasher you'd see one of the connectors going to a metal plate.

If you have a multimeter/continuity tester you can test this by checking the continuity between one of the connectors where the grey cable plugs in at the dishwasher and the chassis. The corresponding connector will be connected to the green wire.

This is done to reduce mistakes and questions from people who don't know here the green wire goes.

Besides that the black cable should be clamped down with a strain relief to remove stress on the copper wires. That would lead to bad connection arcing and general fire hazard.