Electric guitar pickups are really nothing more than specialized microphones that use a type of transducer that senses the movement and frequency of the guitar strings and converts that to an electrical impulse rather than the type of transducer that you would find in a hand held microphone, which picks up actual sound. Neither of them have the amplifier sending current thru them. They both send very weak signals to an amplification system which has to amplify them quite a bit to be useful.
Open systems vs closed systems is really more applicable to pumps and that sort of thing. Every circuit is a "closed system", if you will. If you leave out a piece of the circuit out, then it won't work. It's basically a loop. If you connect one terminal of a light bulb to the postive on a battery but don't connect the other terminal to the negative on the battery, nothing will happen.
In the case of the electric guitar, it is sort of an "open system" in the sense that the hot signal gets sent to the amplifier, but the amplifier doesn't need to close the loop, it just takes what is feed to the input and amplifies it. If the loop is open in the amp, then it will try to close it and complete the circuit by using your guitar to send current thru, which means that YOU become the path to ground, which is potentially fatal. The ground on the guitar serves a few purposes - it is there for safety and it also gives the amplifier a reference to ground, which it needs because it is being fed with an alternating current from the guitar pickup(s) and it helps control unwanted noise by shunting it to ground (EMI & RFI). Using hydraulic terminology, it's sort of like a side arm chemical feed to a closed loop pumping system.
Or here is another roughly similar analogy: think of the power section of an amp as a closed loop piping system connected to one side of a heat exchanger. The heat exchanger is the interface between the guitar and the amp, we'll call it the preamp. The other side of the heat exchanger is connected to the open loop pumping system, the guitar. If the heat exchanger were to fail because it ruptured internally, then the two flows would mix and both systems would then be experiencing a massive failure.
Does that make sense?