Yes, for electric current to flow there must be a loop in the circuit. That's why electrical power cords have two wires and 2 prongs.
Since you're just trying to power a low-voltage light bulb, those responding in this thread can best help by suggesting different ways to increase the power, in case you can't get enough from a single generator of the type you described.
Synchronizing two such generators is possible, but as others have said it's difficult to do in practice.
Wrapping more wire around one generator box, as I suggested earlier.
Or, adding a second magnet to one generator box. Assuming you can fit another one in.
Spinning the magnet(s) faster would also be a way to generate more power.
Edit:
It occurs to me that if the magnets in two different generators were attached to a single, long shaft, they would be synchronized.